Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion

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.