Chaotic Transitions In Deterministic And Stochastic Dynamical

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Chaotic Transitions In Deterministic And Stochastic Dynamical Systems

Wit and Mirth  Or  Pills to Purge Melancholy
Author: Emil Simiu
Publisher: Princeton University Press
ISBN: 1400832500
Size: 13.41 MB
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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, 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.
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems
Language: en
Pages: 240
Authors: Emil Simiu
Categories: Mathematics
Type: BOOK - Published: 2014-09-08 - Publisher: Princeton University Press
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
Topics in Quaternion Linear Algebra
Language: en
Pages: 384
Authors: Leiba Rodman
Categories: Mathematics
Type: BOOK - Published: 2014-08-24 - Publisher: Princeton University Press
Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra.
American Journal of Physics
Language: en
Pages:
Authors: Leiba Rodman
Categories: Physics
Type: BOOK - Published: 2002 - Publisher:
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Pages: 300
Authors: Kung-Sik Chan, Howell Tong
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This book discusses dynamical systems that are typically driven by stochastic dynamic noise. It is written by two statisticians essentially for the statistically inclined readers. It covers many of the contributions made by the statisticians in the past twenty years or so towards our understanding of estimation, the Lyapunov-like index,
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Pages: 844
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Categories: Science
Type: BOOK - Published: 2008-05-31 - Publisher: Springer Science & Business Media
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and
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Pages: 500
Authors: IUrii Isaakovich Neimark, I͡Urii Isaakovich Neĭmark, Yu. I. Neimark, Ûrij Isaakovič Nejmark, Jurij I. Nejmark, Polina Solomonovna Landa
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Type: BOOK - Published: 1992 - Publisher: Springer Science & Business Media
This volume is devoted to stochastic and chaotic oscillations in dissipative systems. It first deals with mathematical models of deterministic, discrete and distributed dynamical systems. It then considers the two basic trends of order and chaos, and describes stochasticity transformers, amplifiers and generators, turbulence and phase portraits of steady-state motions
Nonlinear Dynamics of Chaotic and Stochastic Systems
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Pages: 374
Authors: Vadim S. Anishchenko, Vladimir Astakhov, Alexander Neiman, Tatjana Vadivasova, Lutz Schimansky-Geier
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Type: BOOK - Published: 2003-01-22 - Publisher: Springer Science & Business Media
Contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results. Despite the unified presentation of the subject, care has been taken to present the material in largely self-contained chapters.
Dynamics of Markets
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Pages: 209
Authors: Joseph L. McCauley
Categories: Business & Economics
Type: BOOK - Published: 2004-05-06 - Publisher: Cambridge University Press
Text introducing a new empirically-based model of financial market dynamics.
Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems
Language: en
Pages: 512
Authors: Jerome Bastien, Frederic Bernardin, Claude-Henri Lamarque
Categories: Mathematics
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This book contains theoretical and application-oriented methods to treat models of dynamical systems involving non-smooth nonlinearities. The theoretical approach that has been retained and underlined in this work is associated with differential inclusions of mainly finite dimensional dynamical systems and the introduction of maximal monotone operators (graphs) in order to
Bibliography on Chaos
Language: en
Pages: 514
Authors: Shu-yu Zhang
Categories: Science
Type: BOOK - Published: 1991 - Publisher: World Scientific
This volume is a collection of more than 7000 full titles of books and papers related to chaotic behaviour in nonlinear dynamics. Emphasis has been made on recent publications, but many publications which appeared before 1980 are also included. Many titles have been checked with the authors. The scope of