A nonlinear cross diffusion model analysis by using Holling type III functional response to describe fish and zooplankton dynamics taking into account the fishing effect in the ecosystem

In this paper, we analyse a mathematical model of a cross-diffusion and selfdiffusion system describing the dynamics of fish and zooplankton population. A type III Holling functional response was used in the formulation of the model taking into account the effect of fishing in the ecosystem. Satisfactory results concerning the local and global existence properties of the solutions. Persistence conditions as well as the local stability of equilibrium states are established. We have shown in particular that, under certain conditions, cross-diffusion can trigger the emergence of spatial patterns. Numerical experiments are performed to visualize complex spatial patterns and dynamic behaviour in different fish exploited areas.