Title
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Applications of Melnikov Processes in Engineering, Physic,Used
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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, statedependent, 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 firstyear 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.
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- Q: What is the main focus of the book 'Chaotic Transitions in Deterministic and Stochastic Dynamical Systems'? A: The book focuses on the classical Melnikov method and its application to both deterministic and stochastic dynamical systems, explaining transitions in phase space behavior.
- Q: Who is the author of this book? A: The book is authored by Emil Simiu.
- Q: What prior knowledge is required to understand this book? A: No previous exposure to dynamical systems theory or stochastic processes is required; the book is accessible to readers with a first-year graduate course level in applied mathematics.
- Q: What types of noise does the extended Melnikov method address? A: The extended Melnikov method addresses additive, state-dependent, white, colored, and dichotomous noise in stochastic planar systems.
- Q: What are the practical applications discussed in this book? A: Applications range across various fields including physics, mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.
- Q: What is the condition of the book being sold? A: The book is listed as a used book in good condition.
- Q: When was this book published? A: The book was published on January 1, 2002.
- Q: What is the binding type of this book? A: The book is available in hardcover binding.
- Q: How many pages does the book contain? A: The book contains a total of 246 pages.
- Q: Is this book suitable for beginners in dynamical systems? A: Yes, the book is designed to be accessible even for those without prior knowledge of dynamical systems, making it suitable for beginners.