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 - <p>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.</p>