{"product_id":"complexity-and-evolution-of-dissipative-systems-an-analytical-approach-9783110266481","title":"Complexity and Evolution of Dissipative Systems: An Analytical Approach","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book focuses on the dynamic complexity of neural, genetic networks, and reaction diffusion systems. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for on chaos existence for large class of reaction-diffusion systems is given. The book considers viability problems for such systems - viability under extreme random perturbations - and discusses an interesting hypothesis of M. Gromov and A. Carbone on biological evolution. There appears a connection with the Kolmogorov complexity theory. As applications, transcription-factors-microRNA networks are considered, patterning in biology, a new approach to estimate the computational power of neural and genetic networks, social and economical networks, and a connection with the hard combinatorial problems.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eComplexity and evolution of spatially extended systems: analytical approach\u003c\/p\u003e \u003cp\u003eChapter 1: Introduction\u003c\/p\u003e \u003cul\u003e\n\u003cli\u003eDynamical systems \u003c\/li\u003e\n\u003cli\u003eAttractors \u003c\/li\u003e\n\u003cli\u003eStrange attractors \u003c\/li\u003e\n\u003cli\u003eNeural and genetic networks \u003c\/li\u003e\n\u003cli\u003eReaction diffusion systems \u003c\/li\u003e\n\u003cli\u003eSystems with random perturbations and Gromov-Carbone problem\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eChapter 2: Method to control dynamics: Invariant manifolds, realization of vector fields\u003c\/p\u003e \u003cul\u003e\n\u003cli\u003eInvariant manifolds \u003c\/li\u003e\n\u003cli\u003eMethod of realization of vector fields \u003c\/li\u003e\n\u003cli\u003eControl of attractor and inertial dynamics for neural networks\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eChapter 3: Complexity of patterns and attractors in genetic networks Centralized networks and attractor complexity in such network\u003c\/p\u003e \u003cul\u003e\n\u003cli\u003eA connection with computational problems, Turing machines and finite automatons \u003c\/li\u003e\n\u003cli\u003eGraph theory, graph growth and computational power of neural and genetical networks \u003c\/li\u003e\n\u003cli\u003eMathematical model that shows how positional information can be transformed into body plan of multicellular organism \u003c\/li\u003e\n\u003cli\u003eApplications to TF- microRNA networks. Bifurcation complexity in networks\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eChapter 4: Viability problem, Robustness under noise and evolution\u003c\/p\u003e \u003cul\u003e\n\u003cli\u003eHere we consider neural and genetic networks under large random perturbations \u003c\/li\u003e\n\u003cli\u003eViability problem \u003c\/li\u003e\n\u003cli\u003eWe show that network should evolve to be viable, and network complexity should increase \u003c\/li\u003e\n\u003cli\u003eA connection with graph growth theory (Erdos-Renyi, Albert-Barabasi) \u003c\/li\u003e\n\u003cli\u003eRelation between robustness, attractor complexity and functioning speed \u003c\/li\u003e\n\u003cli\u003eWhy Stalin and Putin's empires fall (as a simple illustration) \u003c\/li\u003e\n\u003cli\u003eThe Kolmogorov complexity of multicellular organisms and genetic codes: nontrivial connections \u003c\/li\u003e\n\u003cli\u003eRobustness of multicellular organisms (Drosophila as an example) \u003c\/li\u003e\n\u003cli\u003eA connection with the Hopfield system\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eChapter 5: Complexity of attractors for reaction diffusion systems and systems with convection\u003c\/p\u003e \u003cul\u003e\n\u003cli\u003eExistence of chemical waves with complex fronts \u003c\/li\u003e\n\u003cli\u003eExistence of complicated attractors for reaction diffusion systems \u003c\/li\u003e\n\u003cli\u003eApplications to Ginzburg Landau systems and natural computing \u003c\/li\u003e\n\u003cli\u003eExistence of complicated attractors for Navier Stokes equations\u003cbr\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"De Gruyter","offers":[{"title":"Default Title","offer_id":53516445417815,"sku":"9783110266481","price":123.98,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/complexity-and-evolution-of-dissipative-systems-an-analytical-approach-9783110266481","provider":"Book Curl","version":"1.0","type":"link"}