Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience

Resource Information

The work Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience represents a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.

Label

Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience

Title remainder

applications of Melnikov processes in engineering, physics, and neuroscience

Statement of responsibility

Emil Simiu

Creator

• Simiu, Emil

Subject

• Chaotic behavior in systems
• Differentiable Dynamical Systems
• Differentiable dynamical systems
• Stochastic Processes
• Stochastic systems
• Chaotic Behavior In Systems

Language

eng

Summary

Annotation:

Member of

• Princeton series in applied mathematics

Cataloging source

CaPaEBR

Dewey number

515/.352

LC call number

QA614.8

LC item number

.S55 2002eb

Series statement

Princeton Series in Applied Mathematics

Summary expansion

The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool.The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology