Control Spiral Waves And Study Chaos Feature Of Small-World Network

Pattern is a kind of inhomogeneous macrostructure, spatiotemporal with a certain regularity, and which is universal in nature. As a kind of non-equilibrium pattern, spiral wave can be find in cardiac muscle, the oxidation of CO on platinum, slime aggregates, the chicken retinal, the Belousov-Zhabotinsky(BZ) reaction, hydrodynamics, and so on. Furthermore, spiral waves break will lead to the appearance of spatiotemporal chaos.In some case, the harmfulness of spiral waves and spatiotemporal chaos is not neglect. For example, spiral waves in myocardial electrical signals can lead to tachycardia. When spiral waves breakup, they turn into spatiotemporal chaos, which can lead to ventricular fibrillation, while ventricular fibrillation is extremely serious arrhythmia and become the leading killer in industrialized countries. Therefore, suppression of spiral waves and spatiotemporal chaos in excitable media is of much practical interest. In this paper, the stochastic and asymmetrical coupling method to effectively suppress spiral waves and spatiotemporal chaos is proposed.As an important kind of spatiotemporal nonlinear system, coupled map lattice model is popular in the field of spatiotemporal chaos because it is easily and efficiently implemented on a computer and can apply directly the result of the research in the spatiotemporal chaos. In the late20th century, CML was being used to study space-time dynamic behavior of complex network, there was ever a great upsurge in studies. In these studies, the regular topological structure of CML is usually considered in which lattice point of the coupling way is global coupling or nearest neighbor coupling, and rarely involves random coupling that similar to small-world networks. In recent years, the small world network is network being closely watched because it can better describer real network than completely random model and completely regular network model. People began to research dynamical characteristic of the model which establishes on the base of small-world network topology structure and coupled map lattice, such as spatiotemporal chaos, synchronization, etc., and have made great achievements. In this paper, we will use this topological structure of CML, in which the Coupling way between lattice points according to WS small-world networks, and to study its dynamic behaviors.This paper is divided into three parts:In the first part, after reviewing the reaction-diffusion systems, the pattern of excitable medium, we introducing the basic concept of chaos and the coupled map lattice model. Finally, we show the basic concept and basic model of complex network.In the second part, the stochastic and asymmetrical coupling method to effectively suppress spiral waves and spatiotemporal chaos is proposed. Numerical simulation indicates that the control effect was affected by the parameters coupling strength and stochastic coupling ratio. It is confirmed that two different systems can achieve phase synchronization and complete synchronization via the computation of mean instantaneous phase difference and the Pearson’s coefficient.In the third part, research the coupling strength, random reconnection probability influence on chaotic characteristic of the model which establishes on the base of s small-world network topology structure and coupled map lattice and qualitative description by the maximum Lyapunov exponent. Then the existence of synchronous phenomenon is proves by calculating the mean-square deviation and average synchronization order parameter.