Bifurcation and Chaos

The book 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. It contains important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequence 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.- 3. Unified Approach.- 4. Extensions.- 5 Conclusions.- References.- New Numerical Methods for High Dimensional Hopf Bifurcation Problems.- 1. Introduction.- 2. Static Bifurcation and Pseudo-Arclength Method.- 3. The Numerical Methods for Hopf Bifurcation.- 4. Examples.- References.- Catastrophe Theory and the Vibro-Impact Dynamics of Autonomous Oscillators.- 1. Introduction.- 2. Generalities on Vibro-Impact Dynamics.- 3. The Geometry of Singularity Subspaces.- 4. Continuity of the Poincaré Map of the S/U Oscillator.- References.- Codimension Two Bifurcation and Its Computational Algorithm.- 1. Introduction.- 2. Bifurcations of Fixed Point.- 3. Computational Algorithms.- 4. Numerical Examples.- 5. Concluding Remarks.- References.- Chaos and Its Associated Oscillations in Josephson Circuits.- 1. Introduction.- 2. Model of Josephson Junction.- 3. Chaos in a Forced Oscillation Circuit.- 4. Autonomous Josephson Circuit.- 5. Distributed Parameter Circuit.- 6. Conclusion.- References.- Chaos in Systems with Magnetic Force.- 1. Introduction.- 2. System of Two Conducting Wires.- 3. Multi-Equilibrium Magnetoelastic Systems.- 4. Magnetic Levitation Systems.- References.- Bifurcation and Chaos in the Helmholtz-Duffing Oscillator.- 1. Mechanical System and Mathematical Model.- 2. Behaviour Chart and Characterization of Chaotic Response.- 3. Prediction of Local Bifurcations of Regular Solutions.- 4. Geometrical Description of System Response Using Attractor-Basin Portraits and Invariant Manifolds.-5. Conclusions.- References.- Bifurcations and Chaotic Motions in Resonantly Excited Structures.- 1. Introduction.- 2. Nonlinear Structural Members.- 3. Resonant Motions of Rectangular Plates with Internal and External Resonances.- 4. Summary and Conclusions.- References.- Non-Linear Behavior of a Rectangular Plate Exposed to Airflow.- 1. Introduction.- 2. Mathematical Model.- 3. Threshold Determination of Periodic Oscillations.- 4. Dynamics Past the Hopf Bifurcation Point.- 5. Summary and Concluding Remarks.- References.