A prey-predator system with a characteristic of the predator subject to mutation is studied. The considered model is
where represents the prey– population and , , represents the predator population. The function satisfies the Dirichlet boundary conditions . The function is a logistic term for the growth rate and the coefficients and have specific interpretations.
The authors conclude an evolutionary stable strategy (EES) result for the diffusion coefficient tending to zero (Th. 3.1). It is also proved that there exists such that, for all , there exists an equilibrium solution of the system (1) (Th. 4.1).