Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience / / Emil Simiu

• Autore: Simiu Emil
• Pubblicazione: Princeton, New Jersey : , : Princeton University Press, , 2002; ©2002
• Descrizione fisica: 1 online resource (244 p.)
• Disciplina: 515/.352
• Soggetto topico: Differentiable dynamical systems; Chaotic behavior in systems; Stochastic systems
• Soggetto non controllato: 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; LTI system theory; Limit cycle; Linear differential equation; Logistic map; Marginal distribution; Moduli (physics); Multiplicative noise; Noise (electronics); Nonlinear control; Nonlinear system; Ornstein–Uhlenbeck process; Oscillation; Parameter space; Parameter; Partial differential equation; Perturbation function; Phase plane; Phase space; Poisson distribution; Probability density function; Probability distribution; Probability theory; Probability; Production–possibility frontier; Relative velocity; Scale factor; Shear stress; Spectral density; Spectral gap; Standard deviation; Stochastic process; Stochastic resonance; Stochastic; Stream function; Surface stress; Symbolic dynamics; The Signal and the Noise; Topological conjugacy; Transfer function; Variance; Vorticity
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front matter -- Contents -- Preface -- Chapter 1. Introduction -- PART 1. FUNDAMENTALS -- Chapter 2. Transitions in Deterministic Systems and the Melnikov Function -- Chapter 3. Chaos in Deterministic Systems and the Melnikov Function -- Chapter 4. Stochastic Processes -- Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process -- PART 2. APPLICATIONS -- Chapter 6. Vessel Capsizing -- Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems -- Chapter 8. Stochastic Resonance -- Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- Chapter 10. Snap-Through of Transversely Excited Buckled Column -- Chapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor -- Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System -- Appendix A1 Derivation of Expression for the Melnikov Function -- Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds -- Appendix A3 Topological Conjugacy -- Appendix A4 Properties of Space ∑2 -- Appendix A5 Elements of Probability Theory -- Appendix A6 Mean Upcrossing Rate τu-1 for Gaussian Processes -- Appendix A7 Mean Escape Rate τ∊-1 for Systems Excited by White Noise -- References -- Index
• Sommario/riassunto: 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.
• Titolo autorizzato: Chaotic transitions in deterministic and stochastic dynamical systems
• ISBN: 0-691-05094-5; 1-4008-3250-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910827211303321
• Lo trovi qui: Univ. Federico II
• Serie: Princeton series in applied mathematics.