A Reaction Diffusion Model for Inter-Species Competition and Intra-Species Cooperation

Publisher： Edp Sciences

E-ISSN： 1760-6101|8|3|154-181

ISSN： 0973-5348

Source： Mathematical Modelling of Natural Phenomena , Vol.8, Iss.3, 2013-06, pp. : 154-181

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Abstract

We study a reaction diffusion system that models the dynamics of two species that display inter-species competition and intra-species cooperation. We find that there are between three and six different equilibrium states and a variety of possible travelling wave solutions that can connect them. After examining the travelling waves that are generated in three different ecologically-relevant initial value problems, we construct asymptotic solutions in the limit λ ≪ 1 (fast diffusion, slow reaction for the second species relative to the first).

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