Asymptotic behaviour of monotone multi-valued dynamical systems

Abstract

We introduce the concept of a monotone multi-valued semi-flow as an order-preserving map. This definition is motivated by the applications in the theory of differential equations without uniqueness of solutions. For an order-preserving multi-valued semi-flow we prove several results on the structure of the global attractor. Some applications to models governed by ordinary differential equations and delay equations with continuous right-hand side are presented. In particular, the abstract results are applied to a biochemical control circuit.