Selective Stabilization of Unstable Standing Waves in a Reaction-diffusion System

Abstract

Autonomous pattern formation phenomena are ubiquitous throughout nature. In 6), the authors showed that we can suitably guide such phenomena to effectively generate specific static spatial patterns. In this paper, we attempt to stabilize dynamic patterns under the same philosophy. To this end, we employ a 3-component reaction-diffusion system as a mathematical model, and stabilize prespecified unstable standing waves. The effectiveness of the proposed control law is evaluated theoretically not only in a finite dimensionally truncated dynamics as in 6), but also in the original partial differential equations.