Numerical analysis for one dimensional tyson's reaction-diffusion model

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.