Study of Arbitrary Nonlinearities in Convective Population Dynamics with Small Diffusion

Details Study of Arbitrary Nonlinearities in Convective Population Dynamics with Small Diffusion Study of Arbitrary Nonlinearities in Convective Population Dynamics with Small Diffusion

2005-04-29

arxiv.org/abs/q-bio/0505001v1

Phys. Rev. E 72, 041902 (2005)

Biology

Quantitative Biology

Populations and Evolution

14 pages, 9 figures

Scientific paper

10.1103/PhysRevE.72.041902

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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