Large Amplitude Patterns for Two Competing Species.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Large amplitude solutions are obtained for systems of semilinear reaction-diffusion equations arising in mathematical ecology which describe the evolution of two competing species. Their behavior is locally consistent with the principle of competitive exclusion. Such solutions are first obtained for a special class of steady state equations in which the two species are assumed to be exactly equal competitors large amplitude patterns for generic classes of equations are then obtained by introducing various perturbations in the relative competitive strengths of the two species. In particular, we obtain 1, travelling wave solutions through constant perturbations, and 2, stable stationary solutions through spatially inhomogeneous perturbations. Author
- Theoretical Mathematics