Nonlinear science Books

Book SynopsisThis distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field — including some innovations by the authors themselves — that have not appeared in any other book.The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained.This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.Table of ContentsThis distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.

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Book SynopsisIn the last forty years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of Mathematics in Tianjin of May 2009 reflect this development from different angles. This volume contains articles based on lectures in the following areas of nonlinear analysis: critical point theory, Hamiltonian dynamics, partial differential equations and systems, KAM theory, bifurcation theory, symplectic geometry, geometrical analysis, and celestial mechanics. Combinations of topological, analytical (especially variational), geometrical, and algebraic methods in these researches play important roles. In this proceedings, introductory materials on new theories and surveys on traditional topics are also given. Further perspectives and open problems on hopeful research topics in related areas are described and proposed. Researchers, graduate and postgraduate students from a wide range of areas in mathematics and physics will find contents in this proceedings are helpful.Table of ContentsOn 2-Tori Having a Pole (V Bangert); Turing Patterns and Standing Waves in Fitzhugh-Nagumo Type Systems (C-N Chen & S-Y Kung); Remarks on Mean Value Properties (Y Y Li & L Nguyen); Brake Orbits in Bounded Convex Symmetric Domains (C Liu & D Zhang); Recent Progress on Closed Geodesics in Some Compact Simply Connected Manifolds (Y Long); Topological Bifurcation Theory: Old and New (J Mawhin); Exponential Growth Rate of Paths and Its Connection with Dynamics (Z Xia & P Zhang); Rabinowitz's Theorems Revisited (W Zou); and other papers.

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Book SynopsisNew Edition: The Nonlinear Workbook (6th Edition)The Nonlinear Workbook provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C++, Java and SymbolicC++ implementations. The book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material, more than 100 worked out examples and 150 ready to run programs are included. New topics added to the fifth edition are Langton's ant, chaotic data communication, self-controlling feedback, differential forms and optimization, T-norms and T-conorms with applications.Table of ContentsNonlinear and Chaotic Maps; Time Series Analysis; Autonomous Systems in the Plane; Nonlinear Hamilton Systems; Nonlinear Dissipative Systems; Nonlinear Driven Systems; Controlling of Chaos; Synchronization of Chaos; Fractals; Cellular Automata; Solving Differential Equations; Optimization; Neural Networks; Genetic Algorithms; Gene Expression Programming; Wavelets; Discrete Hidden Markov Processes; Fuzzy Sets and Fuzzy Logic.

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Book SynopsisNew Edition: The Nonlinear Workbook (6th Edition)The Nonlinear Workbook provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C++, Java and SymbolicC++ implementations. The book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material, more than 100 worked out examples and 150 ready to run programs are included. New topics added to the fifth edition are Langton's ant, chaotic data communication, self-controlling feedback, differential forms and optimization, T-norms and T-conorms with applications.Table of ContentsNonlinear and Chaotic Maps; Time Series Analysis; Autonomous Systems in the Plane; Nonlinear Hamilton Systems; Nonlinear Dissipative Systems; Nonlinear Driven Systems; Controlling of Chaos; Synchronization of Chaos; Fractals; Cellular Automata; Solving Differential Equations; Optimization; Neural Networks; Genetic Algorithms; Gene Expression Programming; Wavelets; Discrete Hidden Markov Processes; Fuzzy Sets and Fuzzy Logic.

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Book SynopsisThis book provides a self-contained presentation of the physical and mathematical laws governing complex systems. Complex systems arising in natural, engineering, environmental, life and social sciences are approached from a unifying point of view using an array of methodologies such as microscopic and macroscopic level formulations, deterministic and probabilistic tools, modeling and simulation. The book can be used as a textbook by graduate students, researchers and teachers in science, as well as non-experts who wish to have an overview of one of the most open, markedly interdisciplinary and fast-growing branches of present-day science.Table of ContentsThe Phenomenology of Complex Systems; Deterministic View; Probabilistic Description; Complexity, Entropy and Information; Prediction; Selected Topics; Exercises and Problems; Suggestions for Further Reading.

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Book SynopsisWave or weak turbulence is a branch of science concerned with the evolution of random wave fields of all kinds and on all scales, from waves in galaxies to capillary waves on water surface, from waves in nonlinear optics to quantum fluids. In spite of the enormous diversity of wave fields in nature, there is a common conceptual and mathematical core which allows to describe the processes of random wave interactions within the same conceptual paradigm, and in the same language. The development of this core and its links with the applications is the essence of wave turbulence science (WT) which is an established integral part of nonlinear science.The book comprising seven reviews aims at discussing new challenges in WT and perspectives of its development. A special emphasis is made upon the links between the theory and experiment. Each of the reviews is devoted to a particular field of application (there is no overlap), or a novel approach or idea. The reviews cover a variety of applications of WT, including water waves, optical fibers, WT experiments on a metal plate and observations of astrophysical WT.Table of ContentsWave Turbulence, A Story Far From Over (A C Newell & B Rumpf); Fluctuations of the Energy Flux in Wave Turbulence (S Aumaitre, E Falcon & S Fauve); Wave Turbulence in Astrophysics (S Galtier); Optical Wave Turbulence (S K Turitsyn, S A Babin, E G Turitsyna, G E Falkovich, E V Podivilov & D V Churkin); Wave Turbulence in a Thin Elastic Plates (G During and N Mordant); Gravity Wave Turbulence in a Large Flume (R Bedard, S Lukaschuk & S Nazarenko); Towards a New Picture of Wave Turbulence (V Shrira & S Annenkov).

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Book SynopsisThe investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.Table of ContentsIntroduction: Continuous and Discontinuous Piecewise-Smooth and Especially Piecewise-Linear Models (An Overview). Bifurcations in Piecewise Smooth Systems; General Concepts: Border Collision and Crisis Bifurcations, Map Replacement Technique; Continuous Piecewise-Linear Maps: Bifurcation Structures in Regular and Chaotic Domains; Discontinuous Piecewise-Linear Maps: Period Adding and Bandcount Adding Bifurcation Structures; Discontinuous Piecewise-Linear Maps: Period Increment and Bandcount Increment Bifurcation Structures; Multi-Dimensional Parameter Spaces and Their Organizing Centers.

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Book SynopsisA small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the “reversibility paradox”, with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the authors' approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and “chaos theory” or “nonlinear dynamics” has supplied a useful vocabulary and a set of concepts, which allow a fuller explanation of irreversibility than that available to Boltzmann or to Green, Kubo and Onsager. Clear illustration of concepts is emphasized throughout, and reinforced with a glossary of technical terms from the specialized fields which have been combined here to focus on a common theme.The book begins with a discussion, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory — fractals and Lyapunov instability — are fundamental to the approach.Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers. The generous assortment of examples worked out in the text will stimulate readers to explore the rich and fruitful field of study which links fundamental reversible laws of physics to the irreversibility surrounding us all.This expanded edition stresses and illustrates computer algorithms with many new worked-out examples, and includes considerable new material on shockwaves, Lyapunov instability and fluctuations.Table of ContentsTime Reversibility, Computer Simulation; Algorithms, Chaos, Computation; Gibbs' Statistical Mechanics; Irreversibility; Microscopic versus Macroscopic Approaches; Lyapunov Instability, Fractals; Reversibility Paradox; Perspective.

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Book SynopsisThis penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence.Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the super string S, which contains all random bit strings of finite length as sub-strings. As an illustration of the mathematical subtlety of this amazing discrete testing signal, the super string S is used to prove mathematically, in a trivial and transparent way, that rule 170 is as chaotic as a coin toss.Yet another unexpected new result, among many others, is the derivation of an explicit basin tree generation formula which provides an analytical relationship between the basin trees of globally-equivalent local rules. This formula allows the symbolic, rather than numerical, generation of the time evolution of any local rule corresponding to any initial bit-string configuration, from one of the 88 globally-equivalent local rules.But perhaps the most provocative idea is the proposal for adopting rule 137, over its three globally-equivalent siblings, including the heretofore more well-known rule 110, as the prototypical universal Turing machine.Table of ContentsPeriod-2 Rules; Period-3 Rules, Period-6 Rules, and Permutive Rules.

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Book SynopsisThe main goal is to offer readers a panorama of recent progress in nonlinear physics, complexity and transport with attractive chapters readable by a broad audience. It allows readers to gain an insight into these active fields of research and notably promotes the interdisciplinary studies from mathematics to experimental physics. To reach this aim, the book collects a selection of contributions to the CCT11 conference (Marseille, 23 - 27 May 2011).Table of ContentsPart A Classical Hamiltonian Dynamics: Resonant Interaction of Charges Particles with Electromagnetic Waves (A A Vasiliev, A V Artemyev, A I Neishtadt, D L Vainchtein and L M Zelenyi); Superrelativistic Charged Particles Acceleration by Electromagnetic Waves: Self-Consistent Model (A V Artemyev, L M Zelenyi and V L Krasovsky); Control of Atomic Transport Using Autoresonance (D V Makarov, M Yu Uleysky and S V Prants); Lagrangian Tools to Monitor Chaotic Transport and Mixing in the Ocean (S V Prants, M V Budyansky and M Yu Uleysky); Stochastic Treatment of Finite-N Fluctuations in the Approach Towards Equilibrium for Mean Field Models (W Ettoumi and M-C Firpo); Anomalous Transport and Phase Space Structures (B Meziani, O Ourrad and X Leoncini); Part B Nonlinear and Quantum Physics: Nonlinear Kinetic Modeling of Stimulated Raman Scattering (D Benisti); Occurrence of Mixed-Mode Oscillations in a Dusty Plasma (M Mikikian, H Tawidian and T Lecas); Pattern Formation by Electrostatic Self-Organization of Membrane Proteins (G Boedec, M Jaeger, F Homble and M Leonetti); Quasiperiodic and Intermittent Stochastic Motions in Penetrative Convection (I N Sibgatullin and D V Kuznetsova); Spiral Pattern Formation in a Simple Two-Phase Flow System (H N Yoshikawa, C Mathis, P Maissa and G Rousseaux); Spin Dependent Transport in an Electron Gas with Magnetic Disorder (T Van Den Berg and A D Verga); The Study of Quantum Chaos Through Entanglement Dynamics (L Y Chew); Part C Probablistic and Signal Processing Approaches: Stochastic Solutions of Nonlinear Pde's: Mckean Versus Superprocesses (R Vilela Mendes); Detection and Characterization of Levy Flights in Chaotic Advection Phenomena (B Ricaud, F Briolle and X Leoncini); On the Long Range Correlation in Fbm-Based Signals with Mixed Statistics (A Scipioni and P Rischette); Feynman - Kac Equation for Convection-Dispersion with Mobile and Immobile Walkers (C Choquet and M C Neel); Part D Complex Systems: Propagation of Information on Undirected Dependency Graphs for Road Traffic Inference (C Furtlehner, Y Han, J-M Lasgouttes, V Martin and F Moutarde); Markov Chain Analysis of Musical Dice Games (D Volchenkov and J R Dawin); Unraveling the Tangles of Language Evolution (F Petroni, M Serva and D Volchenkov).

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Book SynopsisSlime mould Physarum polycephalum is a monstrous single cell well known for its task-solving abilities — solves computational geometry and logical problems, navigates robots and generates music.The slime mould could also build motorways, highways and expressways. It is used to analyse transport networks of Africa, Australia, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, The Netherlands, UK and USA. The largest cities are represented by oat flakes and the slime mould is inoculated in a capital. When all oat flakes are covered by the slime mould, the structure of the protoplasmic networks formed are analyzed. In the laboratory experiments and theoretical analyses, intriguing country-specific properties of the motorway networks are uncovered and compared with the man-made and slime mould networks. They are studied as proximity graphs, leading to hierarchies of complexity and bio-rationality of the motorways.The book will inspire novel and original thoughts, paradigms and approaches for re-evaluation of historical findings on the emergence of ancient roads and will help to design future transcontinental pathways. The book is self-contained and does not require any special training or knowledge. This lavishly illustrated text will be appreciated by readers from all walks of life.Table of ContentsIntroduction (Andrew Adamatzky); Methods: How We Made Experiments and Analysed Their Results (Andrew Adamatzky); Trans-African Highways (Andrew Adamatzky and Anne Kayem); Tracing Historical Development of Australian Highways (Andrew Adamatzky and Mikhail Prokopenko); Belgian Transport Networks: Redundancy and Dissolution (Andrew Adamatzky, Bernard De Baets and Wesley Van Dessel); Brazilian Highways from Slime Mould's Point of View (Andrew Adamatzky and Pedro P B De Oliveira); Trans-Canada Slimeways: From Coast to Coast to Coast (Andrew Adamatzky and Selim G Akl); Slime Mould Imitates Highways in China (Andrew Adamatzky, Xin-She Yang and Yu-Xin Zhao); Schlauschleimer auf Autobahnen: The Case of Germany (Andrew Adamatzky and Theresa Schubert); Vie Physarale: Roman Roads With Slime Mould (Emanuele Strano, Andrew Adamatzky and Jeff Jones); Malaysian Expressways: Is There a Logic Behind? (Andrew Adamatzky, Zuwairie Ibrahim, Amar Faiz Zainal Abidin and Badaruddin Muhammad); Physarum Narcotraficum: Mexican Highways and Slime Mould (Andrew Adamatzky, Genaro J Martinez, Sergio V Chapa-Vergara, Rene Asomoza-Palacio and Christopher R Stephens); Physarum in the Netherlands: Responding to the Flood (Andrew Adamatzky, Michael Lees and Peter M A Sloot); Rebuilding Iberian Motorways with Slime Mould (Andrew Adamatzky and Ramon Alonso-Sanz); United Kingdom Road Planning with Slime Mould (Andrew Adamatzky and Jeff Jones); Slimy Interstates in the USA (Andrew Adamatzky and Andrew Ilachinski); The World's Colonisation and Trade Routes Formation (Andrew Adamatzky); Bio-Rationality of Motorways (Andrew Adamatzky, Selim Akl, Ramon Alonso-Sanz, Wesley van Dessel, Zuwairie Ibrahim, Andrew Ilachinski, Jeff Jones, Anne V D M Kayem, Genaro J Martinez, Pedro de Oliveira, Mikhail Prokopenko, Theresa Schubert, Peter Sloot, Emanuele Strano and Xin-She Yang).

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Book SynopsisScience Sifting is designed primarily as a textbook for students interested in research and as a general reference book for existing career scientists. The aim of this book is to help budding scientists broaden their capacities to access and use information from diverse sources to the benefit of their research careers.The book describes why the capacity to access and integrate both linear and nonlinear information has been an important historic feature of pivotal scientific breakthroughs. Yet, it is a process that our students are rarely, if ever, taught in universities. This book goes beyond simply describing the features of great scientific breakthroughs. It discusses the basis for accessing and using nonlinear information in the linear research context. It also provides a series of tools and exercises that can be used to enhance access to nonlinear information for application to research and other endeavors.Topics covered include focal points in scientific breakthroughs, the use of concepts maps in research, use of different vantage points, information as patterns, fractals for the scientist, memory storage and access points, and synchronicities. Young researchers need useful tools to help with a more holistic approach to their research careers. This book provides the useful tools to support flexibility and creativity across a long-term research career.Roald Hoffmann — Winner of the 1981 Nobel Prize in Chemistry — has contributed the to Science Sifting. More information on Professor Hoffmann can be found at .Table of ContentsPreparing for a Fulfilling Research Career; Introduction to Working in Linearity and in Nonlinearity; A History of Nonlinear Scientific Advancement and Breakthroughs; Untapped Research Information; Information Terrains in Learning and Research; Using Fractals and Fractal Dimensions as a Viewfinder; Multiple Intelligences for Acquiring and Using Information; Synchronicities and Other Intersecting Patterns; A Career of Innovation and Inspiration.

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Book SynopsisScience Sifting is designed primarily as a textbook for students interested in research and as a general reference book for existing career scientists. The aim of this book is to help budding scientists broaden their capacities to access and use information from diverse sources to the benefit of their research careers.The book describes why the capacity to access and integrate both linear and nonlinear information has been an important historic feature of pivotal scientific breakthroughs. Yet, it is a process that our students are rarely, if ever, taught in universities. This book goes beyond simply describing the features of great scientific breakthroughs. It discusses the basis for accessing and using nonlinear information in the linear research context. It also provides a series of tools and exercises that can be used to enhance access to nonlinear information for application to research and other endeavors.Topics covered include focal points in scientific breakthroughs, the use of concepts maps in research, use of different vantage points, information as patterns, fractals for the scientist, memory storage and access points, and synchronicities. Young researchers need useful tools to help with a more holistic approach to their research careers. This book provides the useful tools to support flexibility and creativity across a long-term research career.Roald Hoffmann — Winner of the 1981 Nobel Prize in Chemistry — has contributed the to Science Sifting. More information on Professor Hoffmann can be found at .Table of ContentsPreparing for a Fulfilling Research Career; Introduction to Working in Linearity and in Nonlinearity; A History of Nonlinear Scientific Advancement and Breakthroughs; Untapped Research Information; Information Terrains in Learning and Research; Using Fractals and Fractal Dimensions as a Viewfinder; Multiple Intelligences for Acquiring and Using Information; Synchronicities and Other Intersecting Patterns; A Career of Innovation and Inspiration.

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Book SynopsisThis invaluable book is a unique collection of tributes to outstanding discoveries pioneered by Leon Chua in nonlinear circuits, cellular neural networks, and chaos. It is comprised of three parts. The first — cellular nonlinear networks, nonlinear circuits and cellular automata — deals with Chua's Lagrangian circuits, cellular wave computers, bio-inspired robotics and neuro-morphic architectures, toroidal chaos, synaptic cellular automata, history of Chua's circuits, cardiac arrhythmias, local activity principle, symmetry breaking and complexity, bifurcation trees, and Chua's views on nonlinear dynamics of cellular automata. Dynamical systems and chaos is the scope of the second part of the book, where we find genius accounts on theory and application of Julia set, stability of dynamical networks, chaotic neural networks and neocortical dynamics, dynamics of piecewise linear systems, chaotic mathematical circuitry, synchronization of oscillators, models of catastrophic events, control of chaotic systems, symbolic dynamics, and solitons. First hand accounts on the discovery of memristors in HP Labs, historical excursions into ‘ancient memristors’, analytical analysis of memristors, and hardware memristor emulators are presented in the third and final part of the book.The book is quintessence of ideas on future and emergent hardware, analytic theories of complex dynamical systems and interdisciplinary physics. It is a true Renaissance volume where bright ideas of electronics, mathematics and physics enlighten facets of modern science.The unique DVD covers the artistic aspects of chaos, such as several stunningly melodious musical compositions using chaotic atttractors, a virtual gallery of hundreds of colorful attractors, and even a cartoon-like play on the genesis of Chua's circuit that was based on a widely acclaimed performance in Rome and other venues in Italy. In short, it is a veritable kaleiscope of never-before-published historical, pedagogical, and futuristic technical visions on three timely topics of intense interest for both lay readers and experts alike.Table of ContentsCellular Nonlinear Networks, Nonlinear Circuits and Cellular Automata: Genealogy of Chua's Circuit (Peter Kennedy); Impasse Points, Mutators, and Other Chua Creations (Hyongsuk Kim); Chua's Lagrangian Circuit Elements (Orla Feely); From CNN Dynamics to Cellular Wave Computers (Tamas Roska); Contributions of CNN to Bio-Robotics and Brain Science (P Arena and L Patane); From Radio-amateurs' Electronics to Toroidal Chaos (Otto E Rossler and Christophe Letellier); Analyzing the Dynamics of Excitatory Neural Networks by Synaptic Cellular Automata (V Nekorkin, A Dmitrichev, D Kasatkin and V Afraimovich); Dynamical Systems Perspective of Wolfram's Cellular Automata (M Courbage and B Kaminki); The Genesis of Chua's Circuit: Connecting Science, Art and Creativity (F Bertacchini, E Bilotta, G Laria and P Pantano); Nonlinear Electronics Laboratory (NOEL): A Reminiscence (Chai Wah Wu); Bursting in Cellular Automata and Cardiac Arrhythmias (Gil Bub, Alvin Shrier and Leon Glass); Local Activity Principle: The Cause of Complexity and Symmetry Breaking (Klaus Mainzer); Explorations in the Forest of Bifurcation Trees: Route from Chua's circuit to Chua's Memristive Oscillator (Lukasz Czerwinski and Maciej J Ogorzalek); Chua's Nonlinear Dynamics Perspective Cellular Automata (Giovanni E Pazienza); Application of CNN to Brainlike Computing (Bertram E Shi); Ideal Turbulence Phenomenon and Transmission Line with Chua's Diode (E Yu Romanenko and A N Sharkovsky); Dynamical Systems and Chaos: Connectivity of Julia Sets for Singularly Perturbed Rational Maps (Robert L Devaney and Elizabeth D Russell); Structural Transformations and Stability of Dynamical Networks (L A Bunimovich and B Z Webb); Chua's time (Arturo Buscarino, Luigi Fortuna and Mattia Frasca); Chaotic Neural Networks and Beyond (K Aihara, T Yamada and M Oku); Chaotic Neocortical Dynamics (Walter J Freeman); Nonlinear Dynamics of a Class of Piecewise Linear Systems (M Lakshmanan and K Murali); Chaotic Mathematical Circuitry (R Lozi); Chua's Equation was Proved to be Chaotic in Two Years, Lorenz Equation in Thirty Six Years (Bharathwaj Muthuswamy); Toward a Quantitative Formulation of Emergence (G Nicolis); Controlled Synchronization of Chaotic Oscillators with Huygens' Coupling (J Pena-Ramirez, R H B Fey and H Nijmeijer); Using Time-Delay Feedback for Control and Synchronization of Dynamical Systems (K Pyragas, V Pyragas and T Pyragiene); Models of Catastrophic Events and Suggestions to Foretell Them (Yves Pomeau and Martine Le Berre); Synchronization Propensity in Networks of Dynamical Systems (Stefano Fasan and Sergio Rinaldi); Further Progress in Partial Control of Chaotic Systems (Miguel Sanjuan); Phase and Complete Synchronizations in Time-Delay Systems (D V Senthilkumar, M Manju Shrii and J Kurths); Symbolic Dynamics and Spiral Structures due to the Saddle-Focus Bifurcations (Andrey Shilnikov, Leonid Shilnikov and Roberto Barrio); Dynamics of Periodically Forced Mass Point on Constrained Surface with Changing Curvature (Yoshisuke Ueda); Solitons for Describing 3-D Physical Reality: The Current Frontier (Paul J Werbos); Thermal Solitons in 1D and 2D Anharmonic Lattices - Solectrons and the Organization of Non-Linear Fluctuations in Long-Living Dynamical Structures (M G Velarde, W Ebeling, A P Chetverikov); Global Optimizations by Intermittent Diffusion (Shui-Nee Chow, Tzi-Sheng Yang and Hao-Min Zhou); Memristors: How We Found the Missing Memristor (R Stanley Williams); Aftermath of Finding the Memristor (R Stanley Williams); The Singing Arc: The Oldest Memristor? (Jean-Marc Ginoux and Bruno Rossetto); Two Centuries of Memristors (Themistoklis Prodromakis); State Equations for Active Circuits with Memristors (Martin Hasler); Analytical Analysis of Memristive Networks (Torsten Schmidt, Willi Neudeck, Ute Feldmann and Ronald Tetzlaff); Hardware Memristor Emulators (Andrew L Fitch, Herbert H C Iu and Chi K Tse); Leon Chua's Memristor (Guanrong Chen).

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Book SynopsisThis book is the third volume of lecture notes from summer schools held in the small village of Peyresq (France). These lectures cover nonlinear physics in a broad sense. They were given over the period 2004 to 2008. The summer schools were organized by the Institut Non Linéaire de Nice (Nice, France), the Laboratoire de Physique Statistique (ENS Paris, France) and the Institut de Recherche de Physique Hors Equilibre (Marseilles, France). The goal of the book is to provide a high-quality overview on the state of the art in nonlinear sciences, and to promote the transfer of knowledge between the various domains in physics dealing with nonlinear phenomena.Table of ContentsGeneral Relativity for Beginners (Michel Le Bellac); Interface Growth Phenomena (Alain Pocheau); On Different Aspects of Granular Physics (C Josserand, P-Y Lagree and D Lhuillier); Bio-Adhesion (E Perez and F Pincet); Some Examples of Animal Locomotion in Fluids (Mederic Argenina); Stochastic Perturbations of Nonlinear Dispersive Waves (Anne De Bouard); Statistical Mechanics of Two Dimensional and Geophysical Flows (Freddy Bouchet and Antoine Venaille).

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Book SynopsisThis invaluable volume ends the quest to uncover the secret recipes for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor (i.e. after the transients had disappeared) is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables. As befitting the contents aimed at school children, it was found pedagogically appealing to code each truth table by coloring each of the 8 vertices of a cubical graph in red (for binary state 1), or blue (for binary state 0), forming a toy universe of 256 Boolean cubes, each bearing a different vertex color combination.The corresponding collection of 256 distinct Boolean cubes are then segegrated logically into 6 distinct groups where members from each group share certain common dynamics which allow the long-term evolution of the color configuration of each bit string, of arbitrary length, to be predicted painlessly, via a toy-like gaming procedure, without involving any calculation. In particular, the evolution of any bit string bearing any initial color configuration which resides in any one of the possibly many distinct attractors, can be systematically predicted, by school children who are yet to learn arithmetic, via a simple recipe, for any Boolean cube belonging to group 1, 2, 3, or 4. The simple recipe for predicting the time-asymptotic behaviors of Boolean cubes belonging to groups 1, 2, and 3 has been covered in Vols. I, II, ..., V.This final volume continues the recipe for each of the 108, out of 256, local rules, dubbed the Bernoulli rules, belonging to group 4. Here, for almost half of the toy universe, surprisingly simple recipes involving only the following three pieces of information are derived in Vol. VI; namely, a positive integer τ, a positive, or negative, integer σ, and a sign parameter β > 0, or β < 0. In particular, given any color configuration belonging to an attractor of any one of the 108 Boolean cubes from group 4, any child can predict the color configuration after τ generations, without any computation, by merely shifting each cell σ bits to the left (resp. right) if σ > 0 (resp. σ < 0), and then change the color of each cell if β < 0.As in the five prior volumes, Vol. VI also contains simple recipes which are, in fact, general and original results from the abstract theory of 1-dimensional cellular automata. Indeed, both children and experts from cellular automata will find this volume to be as deep, refreshing, and entertaining, as the previous volumes.

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Book SynopsisThis is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science.The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory).Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.Table of ContentsIntroduction; Minimum Mathematical Background; Leading Up to KAM: A Sketch of the History; KAM Theory; KAM in Context: Questions, Consequences, Significance; Other Results in Hamiltonian Perturbation Theory (HPT); Physical Applications; Appendices: Kolmogorov's 1954 Paper; Overview of Low-Dimensional Small Divisor Problems; East Meets West - Russians, Europeans, Americans; Guide to Further Reading; Selected Quotations; Glossary.

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Book SynopsisThe Nonlinear Workbook provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C++, Java and SymbolicC++ implementations. The book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material, more than 100 worked out examples and 160 ready to run programs are included. Each chapter provides a collection of interesting problems. New topics added to the 6th edition are Swarm Intelligence, Quantum Cellular Automata, Hidden Markov Model and DNA, Birkhoff's ergodic theorem and chaotic maps, Banach fixed point theorem and applications, tau-wavelets of Haar, Boolean derivatives and applications, and Cartan forms and Lagrangian.Table of ContentsNonlinear and Chaotic Maps; Time Series Analysis; Autonomous Systems in the Plane; Nonlinear Hamilton Systems; Nonlinear Dissipative Systems; Nonlinear Driven Systems; Controlling of Chaos; Synchronization of Chaos; Fractals; Cellular Automata; Solving Differential Equations; Optimization; Neural Networks; Genetic Algorithms; Gene Expression Programming; Wavelets; Discrete Hidden Markov Processes; Fuzzy Sets and Fuzzy Logic; Swarm Intelligence; Quantum Cellular Automata; Hidden Markov Model and DNA; Birkhoff's Ergodic Theorem and Chaotic Maps; Banach Fixed Point Theorem and Applications; Tau-Wavelets of Haar; Boolean Derivatives and Applications; Cartan Forms and Lagrangian.

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Book SynopsisThis volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering, operations research and image analysis.Table of ContentsVolterra Models of Evolving Dynamical Systems: Volterra Equations of the 1st Kind with Piecewise Continuous Kernels; Volterra Matrix Equations; Volterra Operator Equations of the 1st Kind with Piecewise Continuous Kernels; Generalized Solutions of Volterra Equations with Discountinuous Kernels and Sources; Nonlinear Models, Singularities and Control: Nonlinear Hammerstain Equations; Nonlinear Volterra Operator Equations with Non-Invertable Operator; Nonlinear Differential Equations Near Branching Points; Convex Majorants Method in the Theory of Nonlinear Volterra Equations; Generalized Solutions of Nonlinear Volterra Equations of 1st Kind; Impulse Control of Volterra Models; Integral Models Applications: Volterra Models Applications; Suppression of Moire Patterns for Video Restoration; Integral Models in Electric Power Engineering;

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Book SynopsisThe study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor. From an in-depth introduction to the different types of dissipativity and attraction, the book takes a comprehensive look at the connections between them, and critically discusses applications of general results to different classes of differential equations.The new Chapters 15-17 added to this edition include some results concerning Control Dynamical Systems — the global attractors, asymptotic stability of switched systems, absolute asymptotic stability of differential/difference equations and inclusions — published in the works of author in recent years.Table of ContentsGlobal Attractors of Autonomous and Non-Autonomous Dynamical Systems; The Structure of Levinson Center of Dynamical System; Holomorphic Dynamical Systems and Their Attractors; Method of Lyapunov Functions; Upper Semicontinuity of Attractors; The Relationship Between Pullback, Forward and Global Attractors; Pullback Attractors Under Discretization; Global Attractors of Some Classes of Evolution Equations (Lorenz Systems, Navier-Stokes Equations, V-Monotone Systems, Difference Equations etc.); Linear Almost Periodic Systems; Global Attractors and Asymptotic Stability of Control Systems;

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Book SynopsisThe wave maps system is one of the most beautiful and challenging nonlinear hyperbolic systems, which has captured the attention of mathematicians for more than thirty years now. In the study of its various issues, such as the well-posedness theory, the formation of singularities, and the stability of the solitons, in order to obtain optimal results, one has to use intricate tools coming not only from analysis, but also from geometry and topology. Moreover, the wave maps system is nothing other than the Euler-Lagrange system for the nonlinear sigma model, which is one of the fundamental problems in classical field theory. One of the goals of our book is to give an up-to-date and almost self-contained overview of the main regularity results proved for wave maps. Another one is to introduce, to a wide mathematical audience, physically motivated generalizations of the wave maps system (e.g., the Skyrme model), which are extremely interesting and difficult in their own right.Table of ContentsPhysical Motivation; Geometrical Description; Energy-Type Estimates; Analytical Tools; General Well-Posedness Theory; The Equivariant Problem; Singularity Formation;

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Book SynopsisThis book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations.Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels.The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.Table of ContentsBifurcation and Chaos of Structural Members; Introduction to Chaos and Wavelets; Quantifying Chaos; Simple Chaotic Models; Dissipative Systems; Euler-Bernoulli Beams; Planar Beams; Beams and Temperature/Electric Fields; Beams with Elasto-Plastic Deformations; Multi-Layer Beams; Timoshenko and Sheremetev-Pelekh Beams; Panels and Cylindrical Panels; Plates and Shells; Flexible Axially-Symmetric Shells;

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Book SynopsisThis book is devoted to the study of boundary value problems for nonlinear ordinary differential equations and focuses on questions related to the study of nonlinear interpolation. In 1967, Andrzej Lasota and Zdzisław Opial showed that, under suitable hypotheses, if solutions of a second-order nonlinear differential equation passing through two distinct points are unique, when they exist, then, in fact, a solution passing through two distinct points does exist. That result, coupled with the pioneering work of Philip Hartman on what was then called unrestricted n-parameter families, has stimulated 50 years of development in the study of solutions of boundary value problems as nonlinear interpolation problems.The purpose of this book is two-fold. First, the results that have been generated in the past 50 years are collected for the first time to produce a comprehensive and coherent treatment of what is now a well-defined area of study in the qualitative theory of ordinary differential equations. Second, methods and technical tools are sufficiently exposed so that the interested reader can contribute to the study of nonlinear interpolation.Table of ContentsCompactness Criterion for Solutions of Nonlinear Differential Equations; Conjugate and Right Focal Boundary Value Problems; Nonlocal Boundary Value Problems; Boundary Value Problems for Finite Difference Equations; Boundary Value Problems for Dynamic Equations on Time Scales;

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