The Study Of Pattern Dynamics In Two-Dimensional Oscillatory System

Spatiotemporal pattern,which appears in systems far away from the thermodynamic equilibrium,is a common phenomenon in nature.Non equilibrium pattern is a kind of non uniform macroscopic structure with some regularity in space or time.Nonequilibrium pattern can be static,such as Turing pattern,from Turing on animal skin patterns of thinking;also can be floating,such as traveling wave,spiral wave,target wave.Two kinds of periodic patterns in two dimensional space-time oscillation system are spiral and target wave,although they are in shape very similar to the periodic structure is circular,their formation conditions and sources are not the same.The spiral wave is a kind of spatiotemporal pattern generally exists in nature,can arise spontaneously in the space-time system uniform,its source is a spatiotemporal topological defect;while the formation and stability of target wave exists with uneven persistent excitation source,which is usually a region.The main content of this paper is through the method of numerical simulation and theoretical analysis to study the dynamic behavior of two-dimensional spatiotemporal pattern oscillation system.The first chapter firstly introduces the pattern dynamics,basic concepts and background knowledge of reaction diffusion system and complex Ginzburg-Landau equation(CGLE),and then focuses on the dynamic behavior and propagatation of the spiral and target patterns.Finally,the research progress of pattern dynamics in a coupled system and basic concepts are briefly introduced.In the second chapter,we analyze and discuss the energy eigenvalue of CGLE system,and the main contents of this chapter are given as follows:(i)The energy eigenvalue in the CGLE system can be divided into two parts,corresponding to spiral wave and bulk oscillation.(ii)Positive energy eigenvalue represents the wave propagating outwardly,while negative energy eigenvalue represents the wave propagating inwardly.(iii)A wave with larger energy eigenvalue can generate and exist stably when it competes with another wave or bulk oscillation with smaller energy eigenvalue in the CGLE system.The third chapter studies the competition rules in two-dimensional inhomogeneous medium.The oscillation in inhomogeneous medium,when the slope of the dispersion curve on both sides of the medium are positive,the competition rules in accordance with the wave in homogeneous competition mode.When the slope of the dispersion relation curve: one is positive,the other side is negative,and two dispersion curves intersect at one point,the system emerges an Interface-Selected Wave(ISW).The ISW located on both sides of the border are connected to the medium frequency is higher than the one for the outer spiral wave frequency and lower the side for inward spiral wave frequency.When the slope of the dispersion relation curve: one is positive,the other side is negative,and do not intersect,the coexistence of wave on both sides of the medium.The fourth chapter mainly studies the periodic oscillation behavior of double coupling system.This chapter mainly takes the double coupled CGLE system for spatio-temporal model,and studies the dynamic behavior of target wave with different frequency coupled inward spiral wave,and we found in weak coupling condition,the system response mode will appear target wave,we call the amplitude of target wave.The target wave has a periodic oscillation frequency,we use fast Fourier transform(FFT)focuses on the analysis of the origin of the periodic oscillation frequency.Finally,this chapter studied the synchronization behaviors of target wave with different frequencies coupled inward spiral waves.The fifth chapter summarizes the whole thesis.