Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics (Journal of Partial Differential Equations, 2019)
"In this paper, we propose a nonlinear reaction-diffusion system describing\r the interaction between toxin-producing phytoplankton and fish population. We analyze the effect of cross-diffusion on the dynamics of the system. The mathematical\r study of the model leads us to have an idea on the existence of a solution, the existence\r of equilibria and the stability of the stationary equilibria. Finally, numerical simulations performed at two-dimensions allowed us to establish the formation of spatial\r patterns and a threshold of release of the toxin, above which we talk about the\r phytoplankton blooms."
Keywords: Toxin effect; populations dynamics; predator-prey model; reaction-diffusion system; bifurcation; pattern formation.