Selective pattern formation control: Spatial spectrum consensus and Turing instability approach

Autonomous pattern formation phenomena are ubiquitous throughout nature. The goal of this paper is to show the possibility to effectively generate various desired spatial patterns by guiding such phenomena suitably. To this end, we employ a reaction–diffusion system as a mathematical model, and formulate and solve a novel pattern formation control problem. First, we describe the control objective in terms of spatial spectrum consensus, which enables utilize recent advances on networked control system theory. Next, the effectiveness of the proposed control law is evaluated theoretically by exploiting the center manifold theorem, and also numerically by simulation. The Turing instabilities play a crucial role throughout the paper.