Spiral Dynamics In An Inhomogeneous Bilayer And Control Of Spiral Wave By Peirodic Pulse Trains

Spiral wave is one of the most important patterns, which are far away from balanceablestates, and it is also a common pattern formation in the nature. In many specific systems, theformation and spontaneous instability of the spiral wave will change the original rhythm ofthe system. For example, it is considered that the formation of the spiral wave will result inarrhythmia, while the spontaneous instability of the spiral wave can often lead to ventricularfibrillation in myocardial system. Spiral wave dynamics, which is an important research topicin nonlinear science, has the important theoretical and the practical significance. In this paper,we have researched spiral wave dynamics in the heterogeneous bilayer and dynamicalbehaviors of spiral waves driven by a periodic pulse chain, the main works are as follows.Part one: researching the dynamics of spiral waves in the two coupling FitzHugh-Nagumo (FHN) systems with different parameters (this part focuses on the chapter2of thepaper). In the excitable two-bilayer system, if we take the initial states of twotwo-dimensional layers as a spiral wave and a resting state respectively, it can be found thatthe non-uniform nature will destroy the complete synchronization of spiral waves between theuniform bilayer(in strong interlayer coupling cases), and two spiral waves in bilayer can notbe synchronized in a narrow spiral region, which lie near the wave front or back. The locationand width of the narrow spiral region depend on the excitability of each two-dimensionallayer in the non-uniform bilayer. These results can be explained by the nature of the excitedmedium and the effect of the interlayer coupling. By investigating tip movements of the initialspiral wave under the effect of interlayer coupling, we find that the spiral tip drifts firstly andthen meanders in a small region, and obtain a rule that dominates the change of the drift andmeandering motion with the initial states of spiral waves and the value of excitableparameters. For interlayer coupling of moderate strength, the bilayer can achieve thesynchronization of the resting state. In the excitable-oscillating bilayer system, if we take theinitial states of two two-dimensional layers as a spiral wave and a resting state respectively,the tip motion of spiral wave depends on the variety of instability steady state and interlayercoupling strength according with some certain rules. In the excitable bilayer, if the initialstates of two two-dimensional layers are both taken as spiral states(but their chiralities andcenters are different), many rules are exihibited in the competive and self-organized processof two spiral waves for two cases of uniform and non-uniform biayers. Part two: researching how periodic pulse chains influence the dynamics of spiral waves(the work of this part focused on papers of chapter3). Under the driving of periodic pulsechains, the dynamics of spiral waves change with the period of the chains, pulse lastingduration and pulse intensity according with some certain laws. The eliminating scheme, inwhich the spiral tip is driven to the boundary and disappears from there, can be designed byapplying periodic pulse trains. We have obtained the parameter range of the external forcingfor eliminating spiral waves. Under this case, the tip motion can be explained by combiningthe existence of refractory and vulnerable periods with the characteristics of external forcing.