In this paper, we consider a reaction-diffusion model with homogeneous Neumann
boundary conditions to describe fish and zooplankton dynamics. This model incorporates
a complex Crowley-Martin functional responses. We also introduce two important
elements: fishing and cannibalism effect in the dynamics. In the mathematical
analysis, global attractor, persistence conditions and 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. Furthermore, we derive the conditions for
Hopf bifurcations and Turing instability. Finally, numerical simulations are presented to
illustrate the analytical results in the different fish exploited and unexploited areas.

Population dynamics, fishing effort, prey-predator system, Crowley-Martin functional response, persistence, stability, Hopf bifurcation, turing instability, zooplankton and fish ecosystem.