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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 pattes and a threshold of release of the toxin,above which we talk about the phytoplankton blooms.