dorsal/arxiv
View SchemaA Mechanism for Spatio-Temporal Disorder in Bistable Reaction-Diffusion Systems
| Authors | Aric Hagberg, Ehud Meron |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9612001 |
| URL | https://arxiv.org/abs/patt-sol/9612001 |
Abstract
In bistable systems, the stability of front structures often influences the dynamics of extended patterns. We show how the combined effect of an instability to curvature modulations and proximity to a pitchfork front bifurcation leads to spontaneous nucleation of spiral waves along the front. This effect is demonstrated by direct simulations of a FitzHugh-Nagumo (FHN) model and by simulations of order parameter equations for the front velocity and curvature. Spontaneous spiral-wave nucleation often results in a state of spatio-temporal disorder involving repeated events of spiral wave nucleation, domain spliting and spiral wave annihilation.
{
"annotation_id": "54b0e0d6-dec0-4a72-8855-7868cecb8fba",
"date_created": "2026-03-02T18:00:29.154000Z",
"date_modified": "2026-03-02T18:00:29.154000Z",
"file_hash": "b6949b14389186dd07ee3f02e7b24d9f7a800d4a9b0696771e3f4be750f10e64",
"private": false,
"record": {
"abstract": "In bistable systems, the stability of front structures often influences the\ndynamics of extended patterns. We show how the combined effect of an\ninstability to curvature modulations and proximity to a pitchfork front\nbifurcation leads to spontaneous nucleation of spiral waves along the front.\nThis effect is demonstrated by direct simulations of a FitzHugh-Nagumo (FHN)\nmodel and by simulations of order parameter equations for the front velocity\nand curvature. Spontaneous spiral-wave nucleation often results in a state of\nspatio-temporal disorder involving repeated events of spiral wave nucleation,\ndomain spliting and spiral wave annihilation.",
"arxiv_id": "patt-sol/9612001",
"authors": [
"Aric Hagberg",
"Ehud Meron"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "A Mechanism for Spatio-Temporal Disorder in Bistable Reaction-Diffusion Systems",
"url": "https://arxiv.org/abs/patt-sol/9612001"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "85155381-3a96-42ed-a91b-48f6f154734a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}