The fractional reaction-diffusion system is investigated. The linear stage of the stability is studied for a two-component system with a different order of fractional derivatives for activator and inhibitor. Three different cases are considered: the derivative order for an activator is greater than that for an inhibitor, the inhibitor order derivative is greater than the activator one, and the orders of time derivatives are comparable. Based on the stability analysis, computer simulation of a Bonhoeffer–van der Pol type reaction-diffusion system with fractional time derivatives is performed, and the diversity of the pattern formation phenomena is shown.

• Received 2 March 2008

DOI:https://doi.org/10.1103/PhysRevE.77.066210