Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators

Wavy front dynamics in a three-component reaction-diffusion system with one activator and two inhibitors

An analytic description for traveling waves in a one-dimensional reaction-diffusion system with one activator and two inhibitors and with equal diffusion constants is developed using a piecewise linear approximation for the nonlinear activator reaction term. The case of front waves is examined in more detail, the monotonic and oscillating fronts being separately considered. The corresponding wave profiles are constructed, and the speed equation is obtained and discussed. It is found that the fronts in the three-component model propagate faster than the fronts in the two-component system. The front interaction is studied using numerical calculations. The results show that at head-on collisions two oscillating fronts produce a wavy domain, which spreads in space with time.