Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience.

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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Bibliographic Details
Main Author: Simiu, Emil.
Format: Electronic
Published: Princeton University Press, 2014.
Online Access:Click for online access
Table of Contents:
  • 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 {u2211}2
  • Appendix A5 Elements of Probability Theory
  • Appendix A6 Mean Upcrossing Rate ?u-1 for Gaussian Processes
  • Appendix A7 Mean Escape Rate ????????-1 for Systems Excited by White Noise
  • References
  • Index