FINITE-DIMENSIONAL ASYMPTOTIC BEHAVIOR OF A PREDATOR-PREY MODEL WITH DIFFUSION

Tóm tắt

The predator-prey model is an essential tool in mathematical ecology and specifically
for our understanding of interacting populations in the natural environment. We consider a predatorprey model with variable carrying capacity and cross-diffusion. First, we recall some recent results on
the existence and regularity of inertial manifolds for nonautonomous evolution equations involving
sectorial operators. We then apply the inertial manifold theory to study the finite-dimensional asymptotic
behavior of the above-mentioned predator-prey model