Dissertation > SCIENCE AND > Nonlinear Science

Study on Nonlinear Waves in Excitable Media Using Cellular Automata Models

Author LuSheng
Tutor DengMinYi; KongLingJiang
School Guangxi Normal University
Course Theoretical Physics
Keywords excitable media nonlinear waves Greenberg-Hasting model isotropic cellularautomata
Type Master's thesis
Year 2012
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One of nonlinear scientific research focus is the study on nonlinear waves in excitable media. People study on excitable media through nonlinear waves mainly. The typical nonlinear waves in excited media include the traveling waves, the target waves and the spiral waves. The studies on excitable media have continued for many years, and the results have been applied in medicine, surface science, and so on. In this paper, we have studied the dynamics of nonlinear waves in excitable media using Greenberg-Hasting cellular automata model(G-H model). The paper content is as follows:1. Basing on the G-H model and the Markus’s improved model, an ameliorate model for excitable media is proposed, and the influence of various parameters on the dynamics of system is studied. We have studied how do the parameters affect the evolution behavior of the traveling wave by changing the system parameters. First, we did the computer simulation to study the effect of D on the stability of the pattern, and find that when the other parameters are fixed, for D<0.346, plane waves can not exist in the system; for0.346≤D<0.381, the plane waves in the system are weakly to be broken, and then the system easily falls into the turbulence; for D>0.381, the plane waves are stable and strong enough not to go into the turbulence. Then we studied about the effects of the parameters on the velocity of the travelling waves, and the results show that the velocity increases as D increases, but decreases as6increases. The travelling wave velocity increases as the a increases when α<0.15, and then turns to be constant when α≥0.15.2. Basing on the G-H model, we have studied the dynamic behaviors of spiral waves with considering excitation contribution of the second nearest neighbor cellular. The numerical simulation results show that:(1)when the other parameters are fixed, the system has the same pattern, the same ratio of the excitable cells, and the same period of the cell under the different ω2, which turns to the conclusion that the ω2doesn’t affect the dynamics of the system.(2) The stable spiral wave keeps its stability unchanged when p0is small enough, but as p0increases, the phenomenon such as meandering, breakup and disappearance of the spiral waves appears. On the other hand, the period of cell and the excitability are also related with p0.3. The isotropy of the G-H model can be improved by three methods as follows: (1) The isotropy will be better when the excitable threshold of the system is appropriate. The computer simulation results show that according to the fixed neighbor radius, there is a appropriate excitable threshold to get better isotropy. The reason of this phenomenon is about the neighbor structure as we analyze in the paper.(2) One can improve the system isotropy by changing the spatial distribution of excitable threshold.In the case of the excitable threshold can have one of the two values randomly, the computer simulation results prove that the two values of the threshold and the ratio about them in the system can also affect the isotropy.(3)The isotropy can be improve by using the ameliorate G-H model. The computer simulations have been done under different parameters, and the results show that the isotropy is not sensitive to the value of the cell status number N, but the value of D affect the isotropy evidently, and the reason is analyzed in the text.

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