A reactiondiffusion model for interspecies competition and intraspecies cooperationTools Rasheed, Shaker M. (2013) A reactiondiffusion model for interspecies competition and intraspecies cooperation. PhD thesis, University of Nottingham.
AbstractThis thesis deals with a two component reactiondiffusion system (RDS) for competing and cooperating species. We have analyse in detail the stability and bifurcation structure of equilibrium solutions of this system, a natural extension of the LotkaVolterra system. We find seven topologically different regions separated by bifurcation boundaries depending on the number and stability of equilibrium solutions, with four regions in which the solutions are similar to those in the LotkaVolterra system. We study RDS in the small parameter of the range $0< \lambda \ll 1 $ (fast diffusion and slow reaction), and in a few cases we assume $\lambda=O(1)$. We consider three types of initial conditions, and we find three types of travelling wave solutions using numerical and asymptotic methods. However, neither numerical nor asymptotic methods were able to find a particular travelling wave solution which connects a coexistence state say, $(u_0,w_0)$ to an extinction state $(0,0)$ when $0< \lambda \ll 1 $. This type can be found when the reactiondiffusion system satisfy the symmetry property and $\lambda=1$.
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