Complexity Studies In Coupled Reaction Diffusion Systems

Spiral waves exist widely in nature, which is the most common phenomenon and relatively stable pattern far away from the thermodynamic equilibrium. Reaction-diffusion system is one of the most common system that can produce spiral wave, The investigations of this pattern are very important for both theoretical studies and practical applications due to its universal dynamical behavior. Most of biological systems are multilayer system which conduce different features and functions through the interaction of each other, such as cerebral cortex is composed of 6 different systems, blood vessels, the wall of heart center room with atrial are approximately composed of the double systems which be used as a thin layer structure. This article mainly observe the phenomenon of synchronization and control between drive system and response through double coupling spirals wave in CGLE equation,verify the effectiveness of local coupling control method, study the control method to transform for spiral wave pattern, and also analyze the forming condition of novel pattern in coupling reaction-diffusion system. All above study for the actual application of patterns provides rich theoretical guidance.The first chapter serves as a brief introduction of the basic concepts and background knowledge of the pattern, spiral wave dynamics and the typical excitability systems that conduce to spiral wave. it is described that the formation mechanism and the direction of propagation of spiral waves. This paper has introduce the synchronization and control of spiral wave in the coupling reaction diffusion system, the innovative research progress of pattern in coupling system, respectively.In the second chapter, effectiveness of local coupling control method is verified. First,using stable single spiral wave induced in CGLE successfully to drive multi-spiral wave as response system in two-dimensional reaction diffusion system by local coupling method which will save more space, discover small area oscillation medium can be produce target wave in multi-spiral wave, discuss the size and location of local square control area to theinfluence of spiral wave competition mechanism in detail. The observations of the control effect is better if choice control region near the center of the multi-spiral wave. Next using target wave replace as spiral waves, analyze the control effect to the size of local square control area, the radius of circular control area, the coupling strength, respectively. Above, the local coupling control method is proved feasible through the numerical simulation experiment.The third chapter discusses the formation condition of the amplitude target wave. First,the study was focused on the mechanism of the two different ways which be- called feedback control and sinusoidal periodic oscillation control to produce target wave in the CGLE, the former by entering a real reduction imaginary part control items can create two type of target wave of zero phase velocity and periodic oscillation by changing the different system parameters in CGLE respectively. While the latter implant a local sine wave, only produce a frequency be controlled target wave, which frequency has the linear relationship with the angular velocity of the controller. Then utilize above three different target wave to couple spiral waves in the response system, find only the target wave generated in the turbulence cannot appear periodic oscillation behavior of the amplitude of response system and the coupling strength are not the same to the remaining two target wave to drive single spiral wave lead to amplitude target wave. Then also find the initial target wave always keep similarity characteristic in structure with amplitude target wave. Finally, it is discussed that the formation reason of amplitude target wave, find the relationship among frequencies in the drive layer of initial target wave, driven layer of spiral wave and amplitude of driven layer meetf =f₁-f₀.The last chapter summarizes the whole thesis.