一维Tyson反应扩散模型的数值分析

Numerical Analysis for One Dimensional Tyson's Reaction Diffusion Model

目的 探索有限区域激励介质在反应和扩散机制同时作用下所产生的化学波方法 在一维Tyson反应扩散模型性质分析的基础上,通过数值计算方法给出不同扩散系数下,反应区域内反应物和催化剂浓度的空间分布值及区域内若干点的催化剂和反应物的浓度随时间的变化值结果 得到了浓度分布,从而可以分析出反应扩散系统长时间的存在状态和稳定的周期时空结构,及反应扩散模型中参数对化学波的产生和发展的影响结论 随着扩散系数值的减小,区域浓度分布由一个波变成波串,而波长、波速变小。

Aim To study the travelling reaction diffusion waves in finite excitable medium. Methods The one dimensional Tyson's reaction diffusion model was used. On the basis of nonlinear dynamical analysis of the model, the values of the space distributions for the concentrations of reactant and autocatalyst and the values of the time variations of the reactant and autocatalyst concentrations at certain points in the finite media were given. Results According to the numerical results, the stable periodic spatio temporal construction and spatio temporal behavior were shown. The effect of model parameters on the initiation and development of the chemical waves was also shown. Conclusion As the diffusion coefficient decreases, the concentration distributions become wave trains from one wave. The wavelength and wave speed become small, and the lengths of start time become long.