This paper is aimed at the mathematical formulation, the analysis, and the numerical simulation of a prey-competitor-predator model by taking into account the toxin produced by the phytoplankton species. The mathematical study of the model leads us to have an idea on the existence of solution, the existence of equilibria, and the stability of the stationary equilibria. These results are obtained through the principle of comparison. Finally, the numerical simulations allowed us to establish a threshold of release of the toxin, above which we talk about the phytoplankton blooms.
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 self- and cross-diffusion on the dynamics of the system. The existence, uniqueness and uniform boundedness of solutions are established in the positive octant. The system is analyzed for various interesting dynamical behaviors which include boundedness, persistence, local stability, global stability around each equilibria based on some conditions on self- and cross-diffusion coefficients. The analytical findings are verified by numerical simulation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.