Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Applications of Melnikov Processes in Engineering, Physics, and Neuroscience - Princeton Series in Applied Mathematics 26 by Emil Simiu Details
Melnikov's classical method provides information on the behavior of inevitable plane systems that may exhibit transitions, ie, escape from and capture of preferred areas of phase space. This book develops…
Melnikov's classical method provides information on the behavior of inevitable plane systems that may exhibit transitions, ie, escape from and capture of preferred areas of phase space. This book develops a unified treatment of deterministic and random systems that extend the applicability of the Melnikov method to random rectangular systems that are actually achievable with added, state, white, colored, or bifurcated noise.
Melnikov's new extension method suggests that movements with transitions are chaotic regardless of whether the excitement is inevitable or random. It explains the role of transitions of system characteristics and specific or random induction, a powerful tool for modeling and identification.
The book is designed primarily for readers interested in applications. The required level of preparation is equivalent to a first-year matriculation course in applied mathematics. No previous exposure to the theory of dynamic systems or the theory of random processes is required. The requirements and theoretical developments are presented in the first part of the book.
The second part of the book is dedicated to applications, ranging from physics to mechanical engineering, marine architecture, oceanography, nonlinear control, random resonance, and neuroscience.
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