Vai al contenuto principale della pagina

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



(Visualizza in formato marc)    (Visualizza in BIBFRAME)

Autore: Simiu Emil Visualizza persona
Titolo: Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience / / Emil Simiu Visualizza cluster
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  Visualizza cluster
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
Opac: Controlla la disponibilità qui
Serie: Princeton series in applied mathematics.