Chaotic Transitions in Deterministic and Stochastic Dynamical Systems (eBook)

Applications of Melnikov Processes in Engineering, Physics, and Neuroscience

Emil Simiu (Autor)

eBook Download: PDF

2014
Princeton University Press (Verlag)
978-1-4008-3250-7 (ISBN)

Infos

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.

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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.

Produkt-Details

• Erscheint lt. Verlag: 8.9.2014
• Reihe/Serie: Princeton Series in Applied Mathematics
• Reihe/Serie: Princeton Series in Applied Mathematics
• Zusatzinfo: 94 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• Schlagworte: affine transformation • Amplitude • Arbitrarily large • attractor • autocovariance • Big O notation • central limit theorem • Change of variables • chaos theory • coefficient of variation • Compound Probability • Computational problem • Control Theory • convolution • coriolis force • correlation coefficient • Covariance function • Cross-covariance • Cumulative distribution function • Cutoff frequency • Deformation (mechanics) • Derivative • Deterministic system • Diagram (category theory) • diffeomorphism • differential equation • Dirac delta function • discriminant • Dissipation • Dissipative system • Dynamical system • Eigenvalues and Eigenvectors • Equations of motion • Even and odd functions • Excitation (magnetic) • Exponential decay • extreme value theory • Flow Velocity • Fluid Dynamics • Forcing (recursion theory) • Fourier series • Fourier transform • fractal dimension • frequency domain • gaussian noise • Gaussian process • Harmonic Analysis • Harmonic function • Heteroclinic orbit • Homeomorphism • Homoclinic orbit • Hyperbolic point • inference • Initial Condition • instability • integrable system • Invariant manifold • Iteration • Joint probability distribution • Limit cycle • linear differential equation • logistic map • LTI system theory • Marginal distribution • Moduli (physics) • multiplicative noise • Noise (electronics) • Nonlinear Control • nonlinear system • Ornstein–Uhlenbeck process • Oscillation • Parameter • Parameter Space • partial differential equation • perturbation function • phase plane • Phase space • Poisson distribution • Probability • Probability density function • Probability Distribution • Probability Theory • Production–possibility frontier • relative velocity • Scale factor • shear stress • Spectral density • Spectral Gap • standard deviation • stochastic • Stochastic process • Stochastic Resonance • Stream Function • surface stress • symbolic dynamics • The Signal and the Noise • Topological conjugacy • Transfer Function • Variance • Vorticity
• ISBN-10: 1-4008-3250-0 / 1400832500
• ISBN-13: 978-1-4008-3250-7 / 9781400832507