Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics

Abstract

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In this paper, we propose a nonlinear reaction-diffusion system describing\r\nthe interaction between toxin-producing phytoplankton and fish population. We analyze the effect of cross-diffusion on the dynamics of the system. The mathematical\r\nstudy of the model leads us to have an idea on the existence of a solution, the existence\r\nof equilibria and the stability of the stationary equilibria. Finally, numerical simulations performed at two-dimensions allowed us to establish the formation of spatial\r\npatterns and a threshold of release of the toxin, above which we talk about the\r\nphytoplankton blooms.<\/p>"