TY - JOUR T1 - Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics AU - Ouedraogo , Hamidou AU - Ouedraogo , Wendkouni AU - Sangaré , Boureima JO - Journal of Partial Differential Equations VL - 3 SP - 207 EP - 228 PY - 2019 DA - 2019/10 SN - 32 DO - http://doi.org/10.4208/jpde.v32.n3.2 UR - https://global-sci.org/intro/article_detail/jpde/13340.html KW - Toxin effect KW - populations dynamics KW - predator-prey model KW - reaction-diffusion system KW - bifurcation KW - pattern formation. AB -

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.