Study On The Dynamics Of Spiral Waves In The Coupled Excitable Media

Spiral wave is frequently encountered in nature. They have been observed in many biological, physical and chemical systems, such as cardiac tissues, the chemical Belousov-Zhabotinsky reaction, the self-organization of slime mold aggregation, the waves of calcium ion in oocyte and CO oxidation on platinum, and so on. The investigation of spiral waves in cardiac tissues and other reaction-diffusion systems has been got much attention since the corresponding electrical signal can cause tachycardia if spiral wave occurs in cardiac tissue. The corresponding electrical signal leads to ventricular fibrillation when spiral wave breaks up into complex spatio-temporal patterns, endangering life.The dynamics of spiral wave in single layer excitable medium has been extensively investigated at the present time. Now the dynamics of spiral waves in coupled excitable media is gradually attracted attention since some biological systems are made of multilayer media. For example, the cerebral cortex consists of six layers which have different characteristics and functions. There are different ion currents in cardiac myocytes. When there is the electrical signal of spiral waves in cardiac tissues, the spatial distributions of ion currents are also types of spiral wave. The interaction between ion currents plays important role in the dynamics of spiral waves. The coupling of ion currents can lead to the poor control effects of some control methods, which can successfully suppress spiral waves in some reaction diffusion systems. So it is necessary to study the dynamics of spiral waves in coupled multilayer excitable media.It is found that the cardiac arrhythmia may be induced by the early afterdepolarizations. It is important for the prevention and treatment of heart disease that the effect of the early afterdepolarizations on spiral waves is investigated. However, the problem has not fully investigated up to now.In this paper, we apply Bar model to study the dynamics of spiral waves in excitable media with feedback coupling. The effect of the early afterdepolarizations on spiral wave in an excitable medium is also investigated. This paper is organized as follows:Chapter I is the introduction and summary. The chaotic synchronization, some typical reaction-diffusion systems, the nature of the excitable medium, some excitable system models, the formation of spiral wave, and the synchronization of spatiotemporal patterns in reaction-diffusion system are briefly introduced.Chapterâ…¡investigates the dynamics of spiral wave in response excitable medium system. Unidirectional linear error feedback coupling of two excitable medium systems displaying spiral waves is considered. The spiral wave in the response system is thus subjected to a spiral wave forcing. We find that the unidirectional feedback coupling can lead to richer behavior than the mutual coupling. The spiral wave dynamics in the response system depends on the coupling strength and frequency mismatch. When the coupling strength is small, the feedback coupling induces the drift or meander of the forced spiral wave. When the coupling strength is large enough, the feedback coupling may lead to the transition from spiral wave to anti-target or target-like wave. The generation of anti-target wave in coupled excitable media is observed for the first time. Furthermore, when the coupling strength is strong, the synchronization between two subsystems can be established.The dynamics of spiral wave in a three-layer excitable media with circular feedback coupling is studied by using the Bar model in chapterâ…¢. The numerical results show that the drifting or meandering of spiral waves in the subsystems can be observed when the coupling strength is small. When the coupling strength is slightly big, the interaction between subsystems may cause spiral waves in some subsystems to move out of the boundaries of the subsystems. The subsystems return to rest state. In addition the interaction may generate the transition from spiral wave state to target wave or turbulence states in some subsystems. The phenomenon that the asymptotic state of a subsystem depends on the initiation condition is observed. With the further increase of the coupling strength, the approximate generalized synchronization of the spiral waves in three subsystems is established. When the coupling strength is bigger, the spiral waves evolve into turbulence.The effects of the early afterdepolarizations behavior on spiral wave described by Bar model is investigated in chapter IV through considering some refractory states of the excitable medium can be excited. The numerical results show that when the threshold of depolarization and the depolarization duration are suitably chosen, the depolarization can induce the drifting and meandering of spiral wave, even causes spiral wave to move out of the boundary of the system. The dense spiral wave, two-arm spiral wave, twin speaks wave, multiple spiral wave and spatiotemporal chaos could also be generated by the depolarization. The physical mechanism underlying these phenomena is discussed.