dorsal/arxiv
View SchemaStudy of Arbitrary Nonlinearities in Convective Population Dynamics with Small Diffusion
| Authors | Ignacio D. Peixoto, Luca Giuggioli, V. M. Kenkre |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0505001 |
| URL | https://arxiv.org/abs/q-bio/0505001 |
| DOI | 10.1103/PhysRevE.72.041902 |
| Journal | Phys. Rev. E 72, 041902 (2005) |
Abstract
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for the evolution of population densities. The initial value problem is solved explicitly for some cases and for others it is shown how to find traveling wave solutions analytically. The effect of adding diffusion to the convective equations is first studied through exact analysis through a piecewise linear representation of the nonlinearity. Using an appropriate small parameter suggested by that analysis, a perturbative treatment is developed to treat the case in which the convective evolution is augmented by a small amount of diffusion.
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"abstract": "Convective counterparts of variants of the nonlinear Fisher equation which\ndescribes reaction diffusion systems in population dynamics are studied with\nthe help of an analytic prescription and shown to lead to interesting\nconsequences for the evolution of population densities. The initial value\nproblem is solved explicitly for some cases and for others it is shown how to\nfind traveling wave solutions analytically. The effect of adding diffusion to\nthe convective equations is first studied through exact analysis through a\npiecewise linear representation of the nonlinearity. Using an appropriate small\nparameter suggested by that analysis, a perturbative treatment is developed to\ntreat the case in which the convective evolution is augmented by a small amount\nof diffusion.",
"arxiv_id": "q-bio/0505001",
"authors": [
"Ignacio D. Peixoto",
"Luca Giuggioli",
"V. M. Kenkre"
],
"categories": [
"q-bio.PE"
],
"doi": "10.1103/PhysRevE.72.041902",
"journal_ref": "Phys. Rev. E 72, 041902 (2005)",
"title": "Study of Arbitrary Nonlinearities in Convective Population Dynamics with Small Diffusion",
"url": "https://arxiv.org/abs/q-bio/0505001"
},
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