dorsal/arxiv
View SchemaPropagation failure of traveling waves in a discrete bistable medium
| Authors | Gabor Fath |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9711003 |
| URL | https://arxiv.org/abs/patt-sol/9711003 |
| DOI | 10.1016/S0167-2789(97)00251-0 |
Abstract
Propagation failure (pinning) of traveling waves is studied in a discrete scalar reaction-diffusion equation with a piecewise linear, bistable reaction function. The critical points of the pinning transition, and the wavefront profile at the onset of propagation are calculated exactly. The scaling of the wave speed near the transition, and the leading corrections to the front shape are also determined. We find that the speed vanishes logarithmically close to the critical point, thus the model belongs to a different universality class than the standard Nagumo model, defined with a smooth, polynomial reaction function.
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"abstract": "Propagation failure (pinning) of traveling waves is studied in a discrete\nscalar reaction-diffusion equation with a piecewise linear, bistable reaction\nfunction. The critical points of the pinning transition, and the wavefront\nprofile at the onset of propagation are calculated exactly. The scaling of the\nwave speed near the transition, and the leading corrections to the front shape\nare also determined. We find that the speed vanishes logarithmically close to\nthe critical point, thus the model belongs to a different universality class\nthan the standard Nagumo model, defined with a smooth, polynomial reaction\nfunction.",
"arxiv_id": "patt-sol/9711003",
"authors": [
"Gabor Fath"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1016/S0167-2789(97)00251-0",
"title": "Propagation failure of traveling waves in a discrete bistable medium",
"url": "https://arxiv.org/abs/patt-sol/9711003"
},
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