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A Reaction Diffusion Model for Inter-Species Competition andIntra-Species Cooperation

Published online by Cambridge University Press:  12 June 2013

S. M. Rasheed  and
J. Billingham
S. M. Rasheed*
Affiliation:
School of Mathematical Sciences, The University of Nottingham University Park, Nottingham NG7 2RD, UK University of Zakho, Department of Mathematics, Zakho, Kurdistan Region, Iraq
J. Billingham
Affiliation:
School of Mathematical Sciences, The University of Nottingham University Park, Nottingham NG7 2RD, UK
*
⋆ Corresponding author. E-mail: [email protected]
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Abstract

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

Keywords

Reaction-diffusionTravelling wave solutions
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 3: Front Propagation , 2013 , pp. 154 - 181
Copyright
© EDP Sciences, 2013

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