Resonant pattern formation in reaction diffusion System

Abstract

As a model of complex system, reaction diffusion system is studied. In particular, we investigate the effect of external forcing and resonant pattern dynamics. For local reaction, oscillatory and chaotic bistable cases are considered. In addition, patterns in the vertically oscillated granular systems are studied as one of the examples of the forced system where competition between intrinsic local dynamics and coupling is important. For the oscillatory media, a variant of complex Ginzburg-Landau equation is used to describe resonant patterns and frequency locking phenomena. The model exhibits a variety of frequency locked patterns including flats, π fronts, labyrinthine patterns and 2π/3 fronts. We also observe the novel patterns such as bursting domains and target patterns during the transition to locking. The Arnol``d tongue structure, characteristics of the resonant patterns and transitions between them are studied. We show that diffusive couplings, which causes frequency change, can induce or suppress frequency locking. In coupled chaotic bistable systems such as Lorenz and Chua oscillators, two-phase domains are formed. The dynamics of each domain is confined to one phase and typically exhibits two types of behavior: oscillation death or nearly periodic oscillations. We elucidate the role of intrinsic broad time scales on the confinement and the oscillation death. Also the effect of external forcing is investigated. For granular patterns, based on the mass and momentum conservation law, we present a simple continuum model to explain the transition between squares and stripes in vertically oscillated granular layers. The study shows that the transition depends on a competition between lateral movement and the local saturation. The large lateral transfer leads to squares formation, however the local saturation prohibits it and stripes form. We also observe the crossroll and the zigzag instability. By introducing the period doubling bifurcation, hexagonal ...