Description
Book SynopsisThis book is primarily an attempt to familiarize the reader with nonlinear systems, in particular qualitative characteristics in a variety of systems amenable to mathematization. Differential equations form the bulk of the book, while the basics of nonlinearities are presented through theorems and problems, aiming to bring out the essence of some aspects of nonlinearities in the emerging discipline of mathematical science. Qualitative studies that reflect the evolution of nonlinearities have not thus far been approached in this way.
Table of ContentsPreface; Preamble; Motivation; Recapturing linear ordinary differential equations; Linear systems: qualitative behaviour; Stability studies; Study of equilibria: another approach; Non-linear vis a vis linear systems; Stability aspects: Liapunov's direct method; Manifolds: introduction and applications in nonlinearity studies; Periodicity: orbits, limit cycles, Poincare map; Bifurcations: a prelude; Catastrophes: a prelude; Theorizing, further, bifurcations and catastrophes; Dynamical systems; Epilogue; Appendix I; Appendix II; Appendix III; Appendix IV; Appendix V
