Methods of qualitative theory in nonlinear dynamics - Shilnikov, Leonid P.; Shilnikov, Andrey L.; Turaev, Dmitry V.; Chua, Leon O. (World scientific series on nonlinear science, 1998)
Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in the book have been developed only recently and have not yet appeared in textbook form.In keeping with the self-contained nature of the book, all the topics are developed with introductory background and complete mathematical rigor. Generously illustrated and written at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.Sample Chapter(s)Introduction to Part II (124 KB)Chapter 7.1: Rough systems on a plane. Andronov-Pontryagin theorem (218 KB)Chapter 7.2: The set of center motions (158 KB)Chapter 7.3: General classification of center motions (155 KB)Chapter 7.4: Remarks on roughness of high-order dynamical systems (136 KB)Chapter 7.5: Morse-Smale systems (435 KB)Chapter 7.6: Some properties of Morse-Smale systems (211 KB)Contents:Structurally Stable SystemsBifurcations of Dynamical SystemsThe Behavior of Dynamical Systems on Stability Boundaries of Equilibrium StatesThe Behavior of Dynamical Systems on Stability Boundaries of Periodic TrajectoriesLocal Bifurcations on the Route Over Stability BoundariesGlobal Bifurcations at the Disappearance of a Saddle-Node Equilibrium States and Periodic OrbitsBifurcations of Homoclinic Loops of Saddle Equilibrium StatesSafe and Dangerous BoundariesReadership: Engineers, students, mathematicians and researchers in nonlinear dynamics and dynamical systems.