Chaotic Transitions in Deterministic and Stocha, Simiu Paperback^+

Chaotic Transitions in Deterministic and Stochastic Dynamical SystemsApplications of Melnikov Processes in Engineering, Physics, and Neuroscience\nAuthor(s): Emil Simiu\nFormat: Paperback\nPublisher: Princeton University Press, United States\nImprint: Princeton University Press\nISBN-13: 9780691144344, 978-0691144344\nSynopsis\nThe classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, [url] 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 transiti.