Chaos In Coupled Map Lattices Research Articles

Synchronous Chaos in Coupled Map Lattices with General Connectivity Topology

The purpose of the paper is to address the synchronous chaos in coupled map lattices with general connectivity topology. Our main results contain the following. First, the master stability functions also hold for general connectivity topology with coupling through a nonlinear function that needs to be exactly the individual chaotic map. Second, the synchronization curve, composed of pieces of transverse Lyapunov exponent curves, is constructed. Third, necessary and sufficient conditions on coupling strength for yielding the synchronous chaos of the system are given. Moreover, the coupling strength $d_c$ giving the fastest convergence rate of the initial values toward the synchronous state is explicitly obtained. It is also proved that such $d_c$ is independent of the choice of the individual map. Finally, our results here can be applied to address questions of wavelength bifurcations and size instability.

Controlling Spatiotemporal Chaos in Coupled Map Lattices to Periodic Orbits**The project supported by National Natural Science Foundation of China under Grant Nos. 60074020 and 90203008, and the Doctoral Foundation of the Ministry of Education of China

Two methods are presented for controlling spatiotemporal chaotic motion in coupled map lattices to a kind of periodic orbit where the dynamical variables of all lattice sites are equal and act periodically as time evolves. Stability analysis of the periodic orbits is presented. We prove that especially the second controlling method can stabilize all the periodic orbits we concern. Basin of attraction and noise problem are discussed.

Global and Local Control of Spatiotemporal Chaos in Coupled Map Lattices

We present a simple method, using constant pinnings, to suppress spatiotemporal chaos and achieve global control in coupled map lattice models under different situations, e.g., for uniform pinning, nonuniform pinning with regular or random distributions, and lattices with spatial heterogeneity in local dynamics and coupling strength. The method is easy to implement and does not require any a priori information of the system dynamics or explicit changes in its parameters. This method can also be used for local control of spatiotemporal dynamics, an aspect that has crucial importance in many natural systems.