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A Reaction Diffusion Model for Inter-Species Competition and Intra-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: pmxsr2@exmail.nottingham.ac.uk
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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).

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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