The Effects Of Defect On The Dynamics Of Rotating Spiral Wave

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. It is very important to deeply study the formation and the dynamics of spiral wave. In this master thesis, we focus on the study of effects of single circular defect on the dynamics of rotating spiral wave, as well as the diffraction of spiral wave in the system composed by two excitable media with different excitability.The first chapter mainly reviews the excitable systems, the modified FHN model and the recent development about the effects of defect on the spiral wave.And the second chapter gives a systematic discussion about the dynamics and the breakup of spiral wave.The third chapter gives a systematic research of the effects of a single circular defect on the dynamics of rotating spiral wave, while the defect center is enough far away from the center of spiral wave and the distance from the defect center to the center of spiral wave tip is a constant. The numerical simulations indicate that, if the defect radius is enough small, there are no effects on the spiral wave tip. Increasing the radius of the defect, there are two critical radiuses, r_d1 and r_d2 When r_d< r_d1, the end tip trace is drifted slowly with r_d. When r_d= r_d1, the end tip trace will be drifted greatly, compared with the end tip trace at r_d< r_d1. Then if r_d is still increased, the end tip trace will be drifted slowly with the r_d again, compared with the end trace at r_d1. When r_d=r_d2, the tip will be disappeared after the defect is imposed on the media. It is also found that, if the spiral wave tip is not disappeared, the end spiral wave will be stable after a long transient, and the tip trace is still a circle as well as the period of tip is not changed.The effects of different defects on the dynamics of rotating spiral wave are studied in the...