@Article{JPDE-32-207, author = {Ouedraogo , HamidouOuedraogo , Wendkouni and Sangaré , Boureima}, title = {Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {32}, number = {3}, pages = {207--228}, abstract = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n3.2}, url = {http://global-sci.org/intro/article_detail/jpde/13340.html} }