Anti-synchronization And Amplitude Death In Coupled Chaotic Oscillators

Rich dynamics of the chaotic systems had been explored and revealed by the researchers since great efforts had been stress on the nonlinear dynamics research. The method of chaos control and the synchronization of chaotic systems had been rapidly developed since the two reports on the physics review letter about chaos control and chaos synchronization was released by Peccora. Rich dynamics had been found in the coupled chaotic oscillators such as various of synchronization (including complete synchronization, phase synchronization, generalized synchronization, lagged synchronization, partial synchronization, intermittent lagged synchronization, measure synchronization of the coupled Hamiltonian systems etc) and the amplitude death caused by parameter mismatches or time delay in the coupled systems. It is significant to explore these dynamics for its perspective applications in chaos control and security communications. In this article, several dynamics of the coupled chaotic oscillators and corresponding inner regimes of those dynamics are explored carefully including various synchronization dynamics (phase synchronization, anti-synchronization) and amplitude death dynamics. Detailed dynamics are explored theretically and experimentally such as (1) the dynamics of phase synchronization (PS) and necessary conditions of PS in the signal driving chaotic oscillators. (2) Rich dynamics of the coupled chaotic oscillators with various coupling scheme are explored in detail such as the anti-synchronization and partial or complete amplitude death. (3) The patterns with pulses and kinks are explored in the coupled map lattices and the stability of the pulses structure is analyzed proximately by the modes method and the regimes of the stability losing are explored in the pulses and kinks structure. This paper is arranged as follows:In the first chapter, the background and recent progresses of the chaos synchronization theory are introduced briefly and various phenomena of chaos synchronization and their characteristics are shown.In the second chapter, phase synchronization of the chaotic oscillators driven by the periodical signals such as sine wave, pulse wave with different parameter (frequency, amplitude, duty circle) are explored extensively in electronics experiment. Moreover, phase synchronization between two chaotic oscillators driven by the common signals such as the noise or the directed voltage is explored.In the third chapter, the dynamics of anti-synchronization are explored in various coupled chaotic oscillators. The necessary conditions and the parameters of the anti-synchronization are presented theoretically. Rich dynamics are found in the anti-synchronization such as the coexistence of multi attractors, riddled basin and on-off intermittency. Transitions to the anti-synchronizations are revealed and the characters of the anti-synchronization are analyzed compared to the complete synchronization. Electronics circuits are set up to observe the anti-synchronization.In the fourth chapter the partial amplitude death and amplitude death of the coupled chaotic oscillators are explored numerically and theoretically. In some specific coupling scheme, the coupled Lorenz oscillators will transit from the reflection symmetry breaking to the translational symmetry breaking till partial amplitude death (some of the variables of the oscillators cease oscillating while others not) with increasing coupling constant. The inner schemes of the partial amplitude death are presented theoretically and the electronics circuits are setup to verify this phenomenon. Moreover, the amplitude death in coupled identical chaotic oscillators without time delay are explored numerically and clarified to three types.In the fifth chapter the random frozened patterns with kink and pulse structure are explored in the coupled map lattices numerically. The stability of these two structures kinks and pulses are analyzed according to the proximate models. Different modes are found important in the formation of the patterns and the inner regimes of the brushlike bifurcation diagrams and the zigzag maximumal lyapunov exponent of the coupled map lattices are explored.Finally the summary of the whole articles are present.