Chaotic Transitions in Deterministic & Stochastic Dynamical System – Applications of Melnikov Processes in Engineering, Physics & Neuroscience: ... (Princeton Series in Applied Mathematics) - Hardcover

Simiu, Emil

Hardcover

ISBN 10: 0691050945 ISBN 13: 9780691050942

Publisher: Princeton University Press, 2002

Synopsis

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.

About this title

About the Author

Emil Simiu is a NIST Fellow. National Institute of Standards and Technology, and Research Professor, Whiting School of Engineering, The Johns Hopkins University. A specialist in flow-structure interaction, he is the coauthor of Wind Effects on Structures and was the 1984 recipient of the Federal Engineer of the Year award.

From the Back Cover

"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

From the Inside Flap

"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

Edition details

• Publisher: Princeton University Press
• Publication date: 2002
• Language: English
• ISBN 10: 0691050945
• ISBN 13: 9780691050942
• Binding: Hardcover
• Number of pages: 240