On a prey–predator reaction–diffusion system with Holling type III functional response

In this paper we study a prey–predator model defined by an initial–boundary value problem whose dynamics is described by a Holling type III functional response. We establish global existence and uniqueness of the strong solution. We prove that if the initial data are positive and satisfy a certain regularity condition, the solution of the problem is positive and bounded on the domain Q=(0,T)×Ω and then we deduce the continuous dependence on the initial data. A numerical approximation of the system is carried out with a spectral method coupled with the fourth-order Runge–Kutta time solver. The biological relevance of the comparative numerical results is also presented.