| In the history of mankind being, the questions of the non-linear have hovered long enough which are filled with both mystical and fascinating. Among them, pattern dynamic system, raised with chaos theory in 1970 s, is one of the important branches of the non-linear science. Spiral wave is ubiquitous in spatiotemporal pattern and is a typical pattern structure in spatiotemporal system, such as chemical, physical and biological systems because of the extraordinary sense made from the research. Studies show that in medical community, some of the heart diseases as arrhythmia which caused by the break of the electrical spiral wave may get the patients killed. The current situation highlights the necessity and urgency of controlling the spiral wave. This paper mainly studies the effect of the new type controller in the 2D spatiotemporal system with different parameters. It also takes the interference based on the former studies between coupled systems into consideration and makes further generalized studies.The complex Ginzburg-Landau equation(CGLE) is a model frequently used for the study of spatiotemporal system, and is one of the common models of reactiondiffusion system. It is a typical spatiotemporal oscillatory medium model. Its futures are: the simple parameter space and the abundant spatiotemporal patterns. In this work, we consider the complex Ginzburg-Landau equation(CGLE) as the spatiotemporal model to study the control of spatiotemporal chaos and spiral waves.The first chapter mainly involves the introductions of the non-linear dynamic system, chaos and pattern dynamic. Besides, the description of the characters and properties of the 2D-CGLE equation. The research progress has been mentioned in this chapter as well.In the second chapter, the effect of the bias planted in the 2D-CGLE system had been further studied through different parameter of the intensity of bias. The result of the numerical simulation shows that the number of the tips in the 2D-CGLE system will be decreased under the effect of the bias. The larger the intensity of the bias, the lower tips number in the system. And the simulation also shows that annihilation of the tips as well as the effective change of the frequency of the 2D-CGLE system caused by the bias.In the third chapter, a new type of non-feedback controlling with self-frequency has been planted into the 2D-CGLE system. The effect caused by the new type controlling in the system has been discussed. A target wave has been generated with new frequency which is different from both frequency in the controller and system. However, the new frequency has the linear relationship with the self-frequency of the controller which means we can plant special frequency into the system on purpose in a way.In the fourth chapter, we mainly focus on the amplitude spiral wave which has been observed only in the coupled CGLE system from the former studies. The differences between amplitude spiral wave in coupled system and the spiral wave in the ordinary spatiotemporal system come from the synchronization of amplitude-phase. The study was focused on introducing a new type controller which has been studied in the last chapter to the driver layer. It appeared that target shape wave has been generated in the driven layer under the weak interference of the new controller in the driver layer. The relationship among frequencies in the driver layer, driven layer and amplitude of driven layer meet W =2 1W -W which has been first raised in the former studies. We have simulation through an error function and concluded this result in general application. In addition, the frequency in the amplitude of the driven layer could be change purposely according to the result in last chapter.The last chapter summarizes the whole thesis. |
PDF Full Text Request