| Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 3, 2013
Front Propagation
|
|
|---|---|---|
| Page(s) | 154 - 181 | |
| DOI | https://doi.org/10.1051/mmnp/20138310 | |
| Published online | 12 June 2013 | |
A Reaction Diffusion Model for Inter-Species Competition and Intra-Species Cooperation
1 School of Mathematical Sciences, The
University of Nottingham University Park, Nottingham
NG7 2RD,
UK
2 University of Zakho, Department of
Mathematics, Zakho,
Kurdistan Region,
Iraq
⋆ Corresponding author. E-mail: pmxsr2@exmail.nottingham.ac.uk
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).
Mathematics Subject Classification: 35K57 / 34B25
Key words: Reaction-diffusion / Travelling wave solutions
© EDP Sciences, 2013
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