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...

Disgrifiad llawn

Wedi'i Gadw mewn:

Manylion Llyfryddiaeth
Prif Awdur:	Simiu, Emil
Fformat:	eLyfr
Iaith:	English
Cyhoeddwyd:	Princeton University Press, 2014.
Pynciau:	Differentiable dynamical systems. Chaotic behavior in systems. Stochastic systems. MATHEMATICS / Applied. Chaotic behavior in systems Differentiable dynamical systems Stochastic systems
Mynediad Ar-lein:	Click for online access

Tabl Cynhwysion:

Frontmatter
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 {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

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

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