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.

Pattern formation self-diffusion crossdiffusion stability analysis numerical simulations