Based On The Dynamics Of The Coupled Map Lattice Of The Complex Network Topology

Over the past decades, dynamical synchronization and control in complex dynamical systems has attracted much attention. A typical case is the coupled map lattices (CML) which are often used as a convenient model to study characteristics of some spatiotemporal systems. In the past, however, most of these works have been concentrated on the CML in which assumes that the coupling configuration is completely regular or random. It is well known that, regular networks and random networks are both useful idealizations, but interactions in real world are neither completely regular nor completely random, and lie in somewhere between the extremes of order and randomness. Recently, complex networks attract more and more attentions from various fields of science and engineering. Scale-free network is one of the most important complex network models, where the degree distribution obeys a power law form,like the Internet and the WWW. Besides the nodes of these networks with a random pattern of connections, some nodes act as"very connected"hubs, a fact that dramatically influences the way of how the network operates.In this dissertation, dynamical synchronization and control in coupled map lattices(CML) with scale-free (SF)topology have been analyzed. The main results are as follows:1.Dynamical behavior in coupled map lattices with regular topology are investigated by using Lyapunov componet.2.Dynamical behavior in coupled map lattice with scale-free topology are investigated in detail. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength is increased linearly as the coupled strength is increased linearly. The CML with SF loses synchronization and intermittency occurs if control strength is greater than the critical feedback strength.