We consider a reaction-diffusion model with homogeneous Neumann boundary conditions to describe fish and zooplankton dynamics. We also introduce two important elements: fishing and cannibalism effect in the dynamics using a non linear functional responses. In the mathematical analysis, global attractor, persistence conditions and the stability of all equilibrium states are studied. We obtained sufficient conditions to ensure the global stability of the non trivial positive state by using a Lyapunov function. Hopf bifurcations and Turing instability are studies. We end by the numerical experiments to illustrate the analytical results in the different fish exploited and unexploited ecosystem.

prey-predator system, non linear functional response, equilibrium stability, Hopf bifurcation and Turing instability, zooplankton-fish ecosystem.