The Study On The Dynamics And Control Of Spiral Wave In Excitable Media

Spatiotemporal pattern, which appears in systems far from thermodynamic equilibrium conditions, is ubiquitous in physical, chemical, and biological systems. Pattern dynamics is a subject which discusses the origin and rule of these patterns, and is one of the important branches in nonlinear science. The spiral wave is a typical example of self-organization behavior in excitable media. In this thesis, we numerically and theoretically study the dynamic behaviors and control of spiral wave patterns in excitable media. Specifically, the thesis is organized as follows:In Chapter1, we firstly introduce the research field of nonlinear science, and then in detail introduce the research history and current situation of pattern and pattern dynamics, and the formation and dynamics of spiral waves are discussed in detail.In Chapter2, We study the motion of a spiral tip controlled by a local periodic forcing (LPF) imposed on a region around the spiral tip in an excitable medium for a FitzHugh-Nagumo-type model. By means of numerical simulation, it is found that the spiral frequency ωf is sensitive to the frequency and size of the LPF. In addition, we show how the drift speed and direction are adjusted by the amplitude and phase of local periodic forcing, which is consistent with a theoretical analysis based on the weak deformation approximation.In Chapter3, based on the Oregonator model, we study numerically the resonant drift of spirals induced by periodic illuminations in excitable media. It is found that the drift directions and velocities of the spiral tip have been controlled by changing the phase differences of the two illuminations on the interface, and the spiral has been forbidden to drift back to the initial region due to the interface. Furthermore, the simulation result seems to be reliable as it is also consistent perfectly with the theoretical analysis based on the weak deformation approximation.In Chapter4, we firstly introduce two kinds of spiral wave instability, i.e. Eckhaus instability and Doppler instability. Secondly, we show that low-energy local periodic forcing (LPF) applied around spiral tip can efficiently suppress meandering behavior and consequently prevent breakup of spiral waves.Conclusions and perspectives are made in Chpter5.