dorsal/arxiv
View SchemaSynchronization, chaos, and breakdown of collective domain oscillations in reaction-diffusion systems
| Authors | C. B. Muratov |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9608005 |
| URL | https://arxiv.org/abs/patt-sol/9608005 |
| DOI | 10.1103/PhysRevE.55.1463 |
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.
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"abstract": "The universal equations describing collective oscillations of the multidomain\npatterns of small period in an arbitrary $d$-dimensional reaction-diffusion\nsystem of the activator-inhibitor type are asymptotically derived. It is shown\nthat not far from the instability leading to the formation of the pulsating\nmultidomain pattern the oscillations of different domains synchronize. In one\ndimension standing and traveling waves of the oscillation phase are realized.\nIn addition to these, in two dimensions target and spiral waves of the\noscillation phase, as well as spatio-temporal chaos of domain oscillations, are\nfeasible. Further inside the unstable region the collective oscillations break\ndown, so the pulsating multidomain pattern transforms into an irregular\npulsating pattern, the uniform self-oscillations, or turbulence. The parameter\nregions where these effects occur are analyzed. The effects of the pattern\u0027s\ndisorder are also studied. The conclusions of the analysis are supported by the\nnumerical simulations of a concrete model. The obtained results explain the\ndynamics of Turing patterns observed in the experiments on\nchlorite-iodide-malonic acid reaction.",
"arxiv_id": "patt-sol/9608005",
"authors": [
"C. B. Muratov"
],
"categories": [
"patt-sol",
"chao-dyn",
"nlin.CD",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.55.1463",
"title": "Synchronization, chaos, and breakdown of collective domain oscillations in reaction-diffusion systems",
"url": "https://arxiv.org/abs/patt-sol/9608005"
},
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