Geodesic
A Reaction Diffusion Model for Inter-Species Competition and Intra-Species Cooperation
S. M. Rasheed1, 2 ; J. Billingham1
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
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 3, pp. 154-181.

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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).
DOI : 10.1051/mmnp/20138310

S. M. Rasheed 1, 2 ; J. Billingham 1

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 
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S. M. Rasheed; J. Billingham. A Reaction Diffusion Model for Inter-Species Competition and Intra-Species Cooperation. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 3, pp. 154-181. doi : 10.1051/mmnp/20138310. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138310/

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