Minimal sets in monotone and concave skew-product semiflows II: Two-dimensional systems of differential equations

Abstract

Recurrent nonautonomous two-dimensional systems of differential equations of ordinary, finite delay and reaction–diffusion types given by cooperative and concave vector fields define monotone and concave skew-product semiflows, whose dynamics is analyzed in this paper. A complete description of all the minimal sets in a very interesting dynamical situation is provided, and some criteria to determine its possible existence and the area on which they lie are given. Suitable examples prove the optimality of the results.