Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Applications of Melnikov Processes in Engineering, Physics, and Neuroscience

Simiu, Emil

ISBN 10: 0691050945 / ISBN 13: 9780691050942

Editore: Princeton: Princeton University Press, 2002

Riguardo questo articolo

A graduate level examination of a unified treatment of extensions of Melnikov processes in various applications. A clean fine trade paperback in decorative boards (hard cover book)/ no dust jacket, as issued.

Codice articolo 656447

Dati bibliografici

• Titolo: Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Applications of Melnikov Processes in Engineering, Physics, and Neuroscience
• Editore: Princeton: Princeton University Press
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 0691050945
• ISBN 13: 9780691050942
• Rilegatura: Brossura
• Edizione: 1st printing of 1st edition.

Descrizione articolo

Riassunto

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.

Dalla quarta di copertina

"The author has chosen an excellent subject, which will probably become a main direction of research in the field of stochastic differential equations. This book is addressed to a wide readership: specialists in dynamical systems and stochastic processes, mathematicians, engineers, physicists, and neuroscientists. The author succeeds in making the material interesting to all these groups of researchers."--Florin Diacu, Pacific Institute for the Mathematical Sciences, University of Victoria