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

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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 appli...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Simiu, Emil (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, New Jersey : Princeton University Press, 2002.
Colección:Princeton series in applied mathematics.
Temas:
Differentiable dynamical systems.
Chaotic behavior in systems.
Stochastic systems.
Dynamique différentiable.
Chaos.
Systèmes stochastiques.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
MATHEMATICS > Applied.
Chaotic behavior in systems
Differentiable dynamical systems
Stochastic systems
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.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Transitions in Deterministic Systems and the Melnikov Function
  • Flows and Fixed Points. Integrable Systems. Maps: Fixed and Periodic Points
  • Homoclinic and Heteroclinic Orbits. Stable and Unstable Manifolds
  • Stable and Unstable Manifolds in the Three-Dimensional Phase Space {x[subscript 1], x[subscript 2], t}
  • The Melnikov Function
  • Melnikov Functions for Special Types of Perturbation. Melnikov Scale Factor
  • Condition for the Intersection of Stable and Unstable Manifolds. Interpretation from a System Energy Viewpoint
  • Poincare Maps, Phase Space Slices, and Phase Space Flux
  • Slowly Varying Systems
  • Chaos in Deterministic Systems and the Melnikov Function
  • Sensitivity to Initial Conditions and Lyapounov Exponents. Attractors and Basins of Attraction
  • Cantor Sets. Fractal Dimensions
  • The Samle Horseshoe Map and the Shift Map
  • Symbolic Dynamics. Properties of the Space [Sigma subscript 2]. Sensitivity to Initial Conditions of the Smale Horseshoe Map. Mathematical Definition of Chaos
  • Smale-Birkhoff Theorem. Melnikov Necessary Condition for Chaos. Transient and Steady-State Chaos
  • Chaotic Dynamics in Planar Systems with a Slowly Varying Parameter
  • Chaos in an Experimental System: The Stoker Column
  • Stochastic Processes
  • Spectral Density, Autocovariance, Cross-Covariance
  • Approximate Representations of Stochastic Processes
  • Spectral Density of the Output of a Linear Filter with Stochastic Input
  • Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process.
  • Frontmatter
  • Contents
  • Preface
  • Chapter 1. Introduction
  • 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
  • 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 ∑
  • Appendix A5 Elements of Probability Theory
  • Appendix A6 Mean Upcrossing Rate x
  • Appendix A7 Mean Escape Rate x
  • References
  • Index.

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