Target patterns in reaction-diffusion systems

AbstractWe consider the general reaction-diffusion system At = F(A) + ϵ DM ▽2A + ϵg(→x, A), 0 < ϵ ⪡ 1, where the small term ϵg(→x, A) represents the effects of localized impurities. We assume that the system At = F(A) has a stable time-periodic solution. Then we construct stable target pattern solutions of the full system. For typical initial conditions we find that these target patterns will arise only if g(→x, A) ≭0. Finally, we determine how target patterns interact and show that higher frequency target patterns eventually engulf neighboring lower frequency target patterns