Dynamics Of Spiral Waves Induced By Periodic Mechanical Deformation With Phase Difference

Spiral waves are widespread and closely related to people's life in the nature.In some ways,spiral waves are detrimental to people's health.Studies have shown that the tremor is caused by the breakup of the spiral wave.The research in this paper is based on the consideration of the actual situation of cardiac tissue.The B(?)r model is used.And the dynamics of spiral waves under the influences of periodic mechanical deformation are studied.In chapter 1,we firstly introduce the concepts related to pattern and reaction diffusion systems.Then,the perturbation of linear stability is introduced.And we describe two types of bifurcations which are usually found in the reaction-diffusion system.In chapter 2,we introduce the formation and propagation of spiral waves.Then we discuss the basic dynamic properties of spiral waves.The dynamic phenomena such as meandering and instability of spiral waves are introduced.Finally,we introduce the common models and some methods of controlling spiral waves.In chapter 3,we study the influence of mechanical deformation on the drift of spiral wave.Simulation studies show that the drift speed of the spiral wave also increases when the wavelength increases,and the drift direction of the spiral wave is the same as its rotation direction.In chapter 4,we study the influence of mechanical deformation on the breakup of spiral wave.The reason why the spiral wave breakup is that the increase in amplitude causes the system to generate KT greater than the critical curvature KC.Simulation studies have shown that when the ratio of ?/?0 is less than 4.0,the value of Ac increases significantly.The reason for this phenomenon is that the spiral wave is ruffled.The reason for this is that the convex portion having a positive curvature is dragged by the concave portion of the wave having a negative curvature,and the spiral wave is broken only at a large amplitude.When the frequency is near 1.5 times the spiral wave frequency,the value of Ac is the smallest.In chapter 5,we make a summary and outlook about this paper.