Spiral Waves And Spatiotemporal Chaos Control In Excitable Media By Using Coupling Method

Pattern is a kind of inhomogeneous, spatiotemporal macro-structure with some laws, to exist in a large number of systems in nature. Spiral wave is a kind of nonequilibrium pattern, which can be found in excitable media, oscillatory media, and bistable(more precisely double metastable) media, including a lot of physical, biological and chemical systems. In some cases spiral waves and spatiotemporal chaos are undesirable because of their harmfulness. Such as the spiral waves in cardiac muscle can be a cause of tachycardia. Repetitious breakup of spiral waves can lead to spatiotemporal chaos, which is believed as a mechanism of ventricular fibrillation (VF). Therefore, effective control methods are needed to control spiral waves and spatiotemporal chaos. In this master thesis, we focus on the study of spiral waves and spatiotemporal chaos control in excitable media by using mutual coupling method and unidirectional coupling method.The first chapter mainly reviews the excitable systems, some models and the recent development about the dynamics and the breakup of spiral waves.The second chapter discusses the control and synchronization of spiral waves and spatiotemporal chaos. Three control methods have been mentioned, such as feedback control method, outside force control method and parameter adjustment control method. The synchronization of spatiotemporal pattern also has been discussed especially focused in two layer coupled excitable model.The third chapter gives a systematic research of the effects of the mutual coupling method on the spatiotemporal chaos synchronization behavior. Complete synchronization can be achieved by using this method. The method to calculate the coupling coefficient is given and the suitable coupling coefficient which complete synchronization can be achieved has been attained. Spatiotemporal chaos is suppressed in two ways by coupling with two systems in different states.The effects of unidirectional coupling method to suppress spiral waves in excitable media are studied in the forth chapter. It is found that this control method has high control efficiency and robust. It adapts to control spiral waves for catalytic CO oxidation on platinum as well as for the FHN model. And the power law n～c^-k of control time steps n versus the coupling strength c for different model has been obtained.