Pure cross-diffusion models: Implications for traveling wave solutions

Details Pure cross-diffusion models: Implications for traveling wave solutions Pure cross-diffusion models: Implications for traveling wave solutions

2008-07-10

arxiv.org/abs/0807.1655v1

Biology

Quantitative Biology

Populations and Evolution

11 pages, 5 figues

Scientific paper

An analysis of traveling wave solutions of pure cross-diffusion systems, i.e., systems that lack reaction and self-diffusion terms, is presented. Using the qualitative theory of phase plane analysis the conditions for existence of different types of wave solutions are formulated. In particular, it is shown that family of wave trains is a generic phenomenon in pure cross-diffusion systems. The results can be used for construction and analysis of different mathematical models describing systems with directional movement.

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