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

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Résumé

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

Mots-clés

Toxin effect; populations dynamics; predator-prey model; reaction-diffusion system; bifurcation; pattern formation.