Synchronization, chaos, and breakdown of collective domain oscillations in reaction-diffusion systems

Abstract

The universal equations describing collective oscillations of the multidomain patterns of small period in an arbitrary $d$-dimensional reaction-diffusion system of the activator-inhibitor type are asymptotically derived. It is shown that not far from the instability leading to the formation of the pulsating multidomain pattern the oscillations of different domains synchronize. In one dimension standing and traveling waves of the oscillation phase are realized. In addition to these, in two dimensions target and spiral waves of the oscillation phase, as well as spatio-temporal chaos of domain oscillations, are feasible. Further inside the unstable region the collective oscillations break down, so the pulsating multidomain pattern transforms into an irregular pulsating pattern, the uniform self-oscillations, or turbulence. The parameter regions where these effects occur are analyzed. The effects of the pattern's disorder are also studied. The conclusions of the analysis are supported by the numerical simulations of a concrete model. The obtained results explain the dynamics of Turing patterns observed in the experiments on chlorite-iodide-malonic acid reaction.

ReVTeX, 14 pages, 12 figures (8 postscipt, 4 gif), submitted to Phys. Rev. E

References in corpus (4)

• Breathing Spots in a Reaction-Diffusion System
• General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
• Scenarios of domain pattern formation in a reaction-diffusion system
• Self-replication and splitting of domain patterns in reaction-diffusion systems with fast inhibitor

Cited by in corpus (4)

• Theory of domain patterns in systems with long-range interactions of Coulomb type
• Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions
• Synchronization and Control of Spatiotemporal Chaos using Time-Series Data from Local Regions
• Instabilities and disorder of the domain patterns in the systems with competing interactions