Nonlinear dynamics of chaotic and stochastic systems : tutorial and modern developments /

Nonlinear dynamics of chaotic and stochastic systems : tutorial and modern developments /

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Bibliographic Details
Imprint:Berlin ; New York : Springer, c2002.
Description:xiii, 374 p. : ill. ; 24 cm.
Language:English
Series:Springer series in synergetics, 0172-7389
Springer series in synergetics (Unnumbered)
Subject:
Dynamics.
Nonlinear theories.
Chaotic behavior in systems.
Stochastic systems.
Chaotic behavior in systems.
Dynamics.
Nonlinear theories.
Stochastic systems.
Format: E-Resource Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/5613684
Hidden Bibliographic Details
Other authors / contributors:Anishchenko, V. S. (Vadim Semenovich), 1943-
ISBN:3540424199 (alk. paper)
Notes:Includes bibliographical references and index.
Table of Contents:
  • 1. Tutorial
  • 1.1. Dynamical Systems
  • 1.1.1. Introduction
  • 1.1.2. The Dynamical System and Its Mathematical Model
  • 1.1.3. Stability - Linear Approach
  • 1.1.4. Bifurcations of Dynamical Systems, Catastrophes
  • 1.1.5. Attractors of Dynamical Systems. Deterministic Chaos
  • 1.1.6. Summary
  • 1.2. Fluctuations in Dynamical Systems
  • 1.2.1. Introduction
  • 1.2.2. Basic Concepts of Stochastic Dynamics
  • 1.2.3. Noise in Dynamical Systems
  • 1.2.4. The Fokker-Planck Equation
  • 1.2.5. Stochastic Oscillators
  • 1.2.6. The Escape Problem
  • 1.2.7. Summary
  • 1.3. Synchronization of Periodic Systems
  • 1.3.1. Introduction
  • 1.3.2. Resonance in Periodically Driven Linear Dissipative Oscillators
  • 1.3.3. Synchronization of the Van der Pol Oscillator. Classical Theory
  • 1.3.4. Synchronization in the Presence of Noise. Effective Synchronization
  • 1.3.5. Phase Description
  • 1.3.6. Summary
  • References
  • 2. Dynamical Chaos
  • 2.1. Routes to Chaos
  • 2.1.1. Introduction
  • 2.1.2. Period-Doubling Cascade Route. Feigenbaum Universality
  • 2.1.3. Crisis and Intermittency
  • 2.1.4. Route to Chaos via Two-Dimensional Torus Destruction
  • 2.1.5. Route to Chaos via a Three-Dimensional Torus. Chaos on T 3 . Chaotic Nonstrange Attractors
  • 2.1.6. Route to Chaos via Ergodic Torus Destruction. Strange Nonchaotic Attractors
  • 2.1.7. Summary
  • 2.2. Synchronization of Chaos
  • 2.2.1. Introduction
  • 2.2.2. Phase-Frequency Synchronization of Chaos. The Classical Approach
  • 2.2.3. Complete and Partial Synchronization of Chaos
  • 2.2.4. Phase Multistability in the Region of Chaos Synchronization
  • 2.2.5. Bifurcation Mechanisms of Partial and Complete Chaos Synchronization Loss
  • 2.2.6. Synchronization of an Ensemble of Chaotic Oscillators
  • 2.2.7. Summary
  • 2.3. Controlling Chaos
  • 2.3.1. Introduction
  • 2.3.2. Controlled Anti-Phase Synchronization of Chaos in Coupled Cubic Maps
  • 2.3.3. Control and Synchronization of Chaos in a System of Mutually Coupled Oscillators
  • 2.3.4. Controlled Chaos Synchronization by Means of Periodic Parametric Perturbations
  • 2.3.5. Stabilization of Spatio-Homogeneous Motions by Parametric Perturbations
  • 2.3.6. Controlling Chaos in Coupled Map Lattices
  • 2.3.7. Summary
  • 2.4. Reconstruction of Dynamical Systems
  • 2.4.1. Introduction
  • 2.4.2. Reconstruction of Attractors from Time Series
  • 2.4.3. Global Reconstruction of DS
  • 2.4.4. Reconstruction from Biological Data
  • 2.4.5. Global Reconstruction in Application to Confidential Communication
  • 2.4.6. Summary
  • References
  • 3. Stochastic Dynamics
  • 3.1. Stochastic Resonance
  • 3.1.1. Introduction
  • 3.1.2. Stochastic Resonance: Physical Background
  • 3.1.3. Characteristics of Stochastic Resonance
  • 3.1.4. Response to a Weak Signal. Theoretical Approaches
  • 3.1.5. Array-Enhanced Stochastic Resonance
  • 3.1.6. Doubly Stochastic Resonance in Systems with Noise-Induced Phase Transition
  • 3.1.7. Stochastic Resonance for Signals with a Complex Spectrum
  • 3.1.8. Stochastic Resonance in Chaotic Systems with Coexisting Attractors
  • 3.1.9. Analog Simulation
  • 3.1.10. Summary
  • 3.2. Synchronization of Stochastic Systems
  • 3.2.1. Introduction
  • 3.2.2. Synchronization and Stochastic Resonance
  • 3.2.3. Forced Stochastic Synchronization of the Schmitt Trigger
  • 3.2.4. Mutual Stochastic Synchronization of Coupled Bistable Systems
  • 3.2.5. Forced and Mutual Synchronization of Switchings in Chaotic Systems
  • 3.2.6. Stochastic Synchronization of Ensembles of Stochastic Resonators
  • 3.2.7. Stochastic Synchronization as Noise-Enhanced Order
  • 3.2.8. Summary
  • 3.3. The Beneficial Role of Noise in Excitable Systems
  • 3.3.1. Coherence Resonance Near Bifurcations of Periodic Solutions of a Dynamical System
  • 3.3.2. Coherence Resonance in Excitable Dynamics
  • 3.3.3. Noise-Enhanced Synchronization of Coupled Excitable Systems
  • 3.3.4. Summary
  • 3.4. Noise-Induced Transport
  • 3.4.1. Introduction
  • 3.4.2. Flashing and Rocking Ratchets
  • 3.4.3. The Adiabatic Approach
  • 3.4.4. The Overdamped Correlation Ratchet
  • 3.4.5. Particle Separation by Ratchets Driven by Colored Noise
  • 3.4.6. Two-Dimensional Ratchets
  • 3.4.7. Discrete Ratchets
  • 3.4.8. Sawtooth-like Media
  • 3.4.9. Making Spatial Structures Using Ratchets
  • 3.4.10. Summary
  • References
  • Index
Gift of the Clinton M. and Dorothy R. Doede Book Fund bookplate
The John Crerar Library bookplate

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