Cooperative random and stochastic differential equations

This is a systematic study of order-preserving (or monotone) random dynamic al systems which are generated by cooperative random or stochastic differen tial equations. Our main results concern the long-term behavior of these sy stems, in particular the existence of equilibria and attractors and a limit set trichotomy theorem. Several applications (models of the control of the protein synthesis in a cell, of gonorrhea infection and of symbiotic inter action in a random environment) are treated in detail.