Synchronization Of Spatiotemporal Chaos In Regular Coupled And Random Coupled Dynamic System

Regular coupled dynamic system is always one of the most important parts in studying nonlinear dynamics. The studies of control and synchronization of spatiotemporal chaos in regular coupled dynamic system are forward topics in nonlinear scientific field. Over the past several years, Random coupled dynamic system has been becoming the research focus gradually, which relate to broadly unknown subjects and have tremendously applying potentialities.In this paper, we first take one-dimensional and two-dimensional coupled acousto-optic bistable map lattice models as the research targets. Using mutual coupling method to realize the synchronization of the spatiotemporal chaos. Then, we consider the one-dimensional coupled acousto-optic bistable map lattice with its connections rewired randomly, and try to investigate the synchronized properties of this new system. Finally, we study the synchronized properties of the random coupled hyperchaotic Lorenz system in which all nodes are five-dimensional oscillators. In addition, we show the synchronized properties which are affected by time-delayed method . The whole paper can be divided into four parts:In the first part, after introducing the coupled map lattice model briefly, we summarize the research development of synchronization and control of spatiotemporal chaos in coupled map lattice model. Then, we present the introduction of small-world networks model in complex system, and the recent achievements on synchronization of this model are described.In the second part, the one-dimensional and two-dimensional coupled map lattices in nonlinear dynamic system are used as the system model. We report a method with which the spatiotemporal chaos can be synchronized using mutual coupling in two Bragg acousto-optic bistable spatial extended systems. The synchronization can be realized by appropriately selecting the mutual coupling strength. Our simulation shows that the synchronization can also be realized under the influence of small random noise , so this method is robustIn the third part, we set up the random coupled acousto-optic bistable system base on the one-dimensional coupled acousto-optic bistable map lattice model by rewiring its connections randomly, and investigate its synchronized properties and the stability of the synchronized results.In the fourth part, we mainly research the synchronization of space time in the random coupled hyperchaotic Lorenz system. We find that all nodes of the system can achieve synchronization spontaneously. we obtain the minimum coupling strength for achieving the synchronization and the functional relationship between the minimum coupling strength and the system parameters. We prove the trajectory of any node is hyperchaotic and the synchronization state is also chaotic by calculating the Lyapunov exponent spectrum. Moreover, the affection of delay time toward random coupled system is investigated. It is shown that all nodes can achieve complete synchronization when the value of the delay time is proper. Our simulation shows the complete synchronization can also be realized under the influence of small random noise, so time-delayed method is robust...