SOME REMARKS ON THE QUALITATIVE PROPERTIES OF SOLUTIONS TO A PREDATOR-PREY MODEL POSED ON NON COINCIDENT SPATIAL DOMAINS

We are interested in the dynamical behaviour of the solution set to a two component reaction-diffusion system posed on non coincident spatial domains. The underlying biological problem is a predator-prey system featuring a non local numerical response to predation involving an integral kernel. Quite interesting while complex dynamics emerge from preliminary numerical simulations, driven both by diffusivities and by the parametric form or shape of the integral kernel. We consider a simplified version of this problem, with constant coefficients, and give some hints on the large time dynamics of solutions.