by Vadim Anishchenko (Saratov State Univ.)

In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.

Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.

All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.

• Stability and Bifurcation of Dynamical Systems
• Numerical Methods of Chaos Investigations
• Inertial Nonlinearity Oscillator. Regular Attractor Bifurcations
• Autonomous Oscillation Regimes in Oscillator
• Quasiattractor Structure and Properties and Homoclinic Trajectories of Autonomous Oscillator
• Two-Frequency Oscillation Breakdown
• Breakdown of Two- and Three-Frequency Quasiperiodic Oscillations
• Synchronization of Chaos
• Nonlinear Phenomena and Chaos in Chua's Circuit
• Bifurcations of Dynamical System in the Presence of Noise
• Chaos Structure and Properties in the Presence of Noise
• Reconstruction of Dynamical Systems from Experimental Data