The Study On Target Waves In Excitable Media Using Cellular Automata Models

Non-equilibrium pattern is a common non-uniform and macro-structure formation in nature. target waves and spiral waves are the most common non-equilibrium pattern formation and can be observed in excitable systems. Such as the heart, the viscosity is gathering mold, chicken retina, platinum catalyst surface oxidation of carbon monoxide, BZ reaction and so on. Target waves can be used to compare with other nonlinear waves and to control other non-linear wave in excitable media as a common wave; in medicine for the treatment of arrhythmias and other heart disease is significance, how to create a new heart to the heart to restore normal target wave source is very important, especially when the sinus node function is lost.In this paper, we mainly study the basic nature of target waves and spirals on the multi-homogeneous medium under the excited states as well as the critical of broken target wave ,self-sustained and so on. Paper content is as follows.The first chapter is introduction. It briefly describes the nature of excitable media, the knowledge of Sinus and cardiac pacemakers, as well as cellular automata and so on.It obtains the threshold of the waveform increased and more and closer to round under the multi-target wave excited with the excitation compared with a single target wave; target wave velocity c before breaking with the increase of excitation threshold K of non-linear decrease, and draw the relevant conclusions:, K∈[ mR+1,(m+1)R], m where is an integer. If m =0,then c = R; If m =1,then velocity values c decrease on the c = R basis of non-linear ; If m =2,then c = R?1; If m =3,then velocity values c decrease on the c = R?1basis of non-linear ;···And so on。At the same time, the change of target wave propagation velocity c and stimulate threshold K will not be affected multi-excited states of the target wave of change under the excitation source of value, and different values of excitation sources, it has the same stimulating; finally arrive in uniform medium excited state under the multi-target wave cycle T and the same number of cellular states N . Chapter III studies the nature of the critical state in excitable media under the multi-excited states of the target wave broken ,and arrive at the relationship of E , N , R ,K , through the custom critical exponent RKlnα=ln to shows that critical nature of the target wave broken, when the number of excited states E are not the same, the broken critical exponent is also different, as well asαincreasing with the E ; when the neighborhood radius R and the number of states N take the centain valuation, changes the value of E,K , as long as the neighbor radius of the same excitation threshold Critical values K for the same, with the number of cellular state has nothing to do, and with the critical values K increased with R increased; when E,N takes fixed values, changes the value of R,K , in the same E , the value of the Different N does not affect the target wave broken threshold.Chapter IV also studies the problem of self-consistent target wave used the Greenberg-Hasting cellular automaton model of excitable media, here is the self-sustainability in the absence of sustained excitation source generated by the case of self-sustaining. The previous studies have shown that only the target wave excitation in a sustained source of excitation can produce self-sustaining target wave, but, after a numer of simulation studies found that when E = N?2 and the excitation source {2 , 3,…,E}in the values in the System, Center Department does not continue to stimulate source under the same target wave can produce self-sustaining and self-sustainability of the target waveform as the excitation threshold K increases and more closer to round; Moreover, E = N?2, K∈[3 ,M], M which is a positive integer, the initial value of excitation sources takes 1, the target wave from the center of the graph has continued to diversify, and different E , N , R ,K values give rise to different target wave waveforms at different centers, but it still has the regularity in time and space, time evolution of cellular cycle T and the number of states N are equal, that is T = N; and symmetry in space.Chapter V of this paper have done a summary and outlook that the wave nature of the target can also be other models to study, but also can take account of external factors, as well as the space dimension to study the nature of the target wave, so that tit is closer to the actual; because of a certain conditions, the target-wave mechain of diversification is not is very clear,these questions have yet to the further studies.