Cooperative systems with respect to arbitrary orderings

Cooperative ordinary differential equations are of importance in the context of monotonicity and comparison theorems. The special qualitative properties of cooperative systems were elucidated by M.W. Hirsch some decades ago. The usual notion of cooperativity is based on the standard ordering in real n-space defined by the cone of positive vectors. In this talk, an extension to general order cones will be presented, and it will be shown that the usual monotonicity and comparison theorems hold. We also exhibit classes of relevant examples that are cooperative with respect to a nonstandard ordering.