Delayed feedback selective pattern formation in reaction-diffusion systems

In the natural world, there exist many autonomous spatially non-uniform patterns. From an engineering point of view, controlling these phenomena is potentially useful to many practical applications. In view of this, the authors formulated and solved a novel feedback control problem of such autonomous spatial patterns based on a specific reaction-diffusion system [5]. In this paper, toward development of an implementable control strategy, we derive a delay-dependent criterion under which the control law obtained in [5] suitably generates the desired spatial patterns. The effectiveness of the theoretical result is verified by numerical simulations.