dorsal/arxiv
View SchemaPattern Formation in Dissipative Nonvariational Systems: The Effects of Front Bifurcations
| Authors | Aric Hagberg, Ehud Meron |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9305007 |
| URL | https://arxiv.org/abs/patt-sol/9305007 |
| DOI | 10.1088/0951-7715/7/3/006 |
| Journal | Nonlinearity 7, 805 (1994) |
Abstract
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally develop in bistable and excitable systems, but may also appear far beyond Hopf and Turing bifurcations. The global behavior of domain patterns strongly depends on the fronts' inner structures. In this paper we study a symmetry breaking front bifurcation expected to occur in a wide class of reaction-diffusion systems, and the effects it has on pattern formation and pattern dynamics. We extend previous works on this type of front bifurcation and clarify the relations among them. We show that the appearance of front multiplicity beyond the bifurcation point allows the formation of persistent patterns rather than transient ones. In a different parameter regime, we find that the front bifurcation outlines a transition from oscillating (or breathing) patterns to traveling ones. Near a boundary we find that fronts beyond the bifurcation can reflect, while those below it either bind to the boundary or disappear.
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"abstract": "Patterns in reaction-diffusion systems often contain two spatial scales; a\nlong scale determined by a typical wavelength or domain size, and a short scale\npertaining to front structures separating different domains. Such patterns\nnaturally develop in bistable and excitable systems, but may also appear far\nbeyond Hopf and Turing bifurcations. The global behavior of domain patterns\nstrongly depends on the fronts\u0027 inner structures. In this paper we study a\nsymmetry breaking front bifurcation expected to occur in a wide class of\nreaction-diffusion systems, and the effects it has on pattern formation and\npattern dynamics. We extend previous works on this type of front bifurcation\nand clarify the relations among them. We show that the appearance of front\nmultiplicity beyond the bifurcation point allows the formation of persistent\npatterns rather than transient ones. In a different parameter regime, we find\nthat the front bifurcation outlines a transition from oscillating (or\nbreathing) patterns to traveling ones. Near a boundary we find that fronts\nbeyond the bifurcation can reflect, while those below it either bind to the\nboundary or disappear.",
"arxiv_id": "patt-sol/9305007",
"authors": [
"Aric Hagberg",
"Ehud Meron"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1088/0951-7715/7/3/006",
"journal_ref": "Nonlinearity 7, 805 (1994)",
"title": "Pattern Formation in Dissipative Nonvariational Systems: The Effects of Front Bifurcations",
"url": "https://arxiv.org/abs/patt-sol/9305007"
},
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