This book presents a new theory on the transition to dynamical chaos for two-dimensional nonautonomous, and three-dimensional, many-dimensional and infinitely-dimensional autonomous nonlinear dissipative systems of differential equations including nonlinear partial differential equations and differential equations with delay arguments. The transition is described from the Feigenbaum cascade of period doubling bifurcations of the original singular cycle to the complete or incomplete Sharkovskii subharmonic cascade of bifurcations of stable limit cycles with arbitrary period and finally to the complete or incomplete homoclinic cascade of bifurcations. The book presents a distinct view point on the principles of formation, scenarios of occurrence and ways of control of chaotic motion in nonlinear dissipative dynamical systems. All theoretical results and conclusions of the theory are strictly proved and confirmed by numerous examples, illustrations and numerical calculations. Sample Chapter(s). Chapter 1: Systems of Ordinary Differential Equations (1,736 KB). Contents: Systems of Ordinary Differential Equations; Bifurcations in Nonlinear Systems of Ordinary Differential Equations; Chaotic Systems of Ordinary Differential Equations; Principles of the Theory of Dynamical Chaos in Dissipative Systems of Ordinary Differential Equations; Dynamical Chaos in Infinitely-Dimensional Systems of Differential Equations; Chaos Control in Systems of Differential Equations. Readership: Graduate students and researchers in complex and chaotic dynamical systems.
Numerous inroads to this research exist for the advanced student. This book offers glimpses into the field with the aim that the results presented illuminate the beauty & excitement to be found.
Dynamics & Stochastics: Festschrift in Honour of M.S. Keane
书名原文:Mathematics of models:Continuous and discrete dynamical systems
Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.
A New Mathematical Framework for the Study of Linkage and Selection
This book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications.
"This book describes methods that reveal its structures and dynamics.
(203) [204] (205 (206 (207) (208) (209) [210 [211] [212 [213 [214] [215] [216 [217] [218] (219) [220) M. Reed and B. Simon, Methods of Modern Mathematical Physics IV. Analysis of Operators, Academic Press, San Diego, 1978.
... and José Seade, Editors, Geometry and dynamics, 2005 Ravi Vakil, Editor, Snowbird lectures in algebraic geometry, 2005 Michael Entov, Yehuda Pinchover, and Michah Sageev, Editors, Geometry, spectral theory, groups, and dynamics, ...
Global Structural Stability of Flows on Open Surfaces