Bifurcation and Chaos Theory and Applications [Paperback]

A collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is self-contained and includes an elementary introduction, an exposition of the state of the art, as well as details of recent theoretical, computational and experimental results. Included among the practical systems analysed are: hysteretic circuits, Josephson circuits, magnetic systems, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This book provides important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequences of chaotic dynamics.Bifurcation and Chaos presents a collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is self-contained and includes an elementary introduction, an exposition of the present state of the art, and details of recent theoretical, computational and experimental results. Included among the practical systems analysed are: hysteretic circuits, Josephson circuits, magnetic systems, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This book contains important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequences of chaotic dynamics.Quantum Chaos and Ergodic Theory.- 1. Introduction.- 2. Definition of Quantum Chaos.- 3. The Time Scales of Quantum Dynamics.- 4. The Quantum Steady State.- 5. Concluding Remarks.- References.- On the Complete Characterization of Chaotic Attractors.- 1. Introduction.- 2. Scaling Behavior.- 2.1 Scale Invariance.- 2.2 Non-unified Approach.- 3. Unified Approach.- 3.1 The Generalized Entropy Function.- 3.2 Hyperbolic Models with Complete Grammars.- 4. Extensions.- 4.1 The NeedlS}