GLOBAL ASYMPTOTIC BEHAVIOR
IN SOME COOPERATIVE SYSTEMS
OF FUNCTIONAL DIFFERENTIAL EQUATIONS

XIAO-QIANG ZHAO AND ZHU-JUN JING

Abstract. This paper is devoted to the study of global asymptotic behavior in some cooperative systems of functional differential equations. We first prove a general global result for both discrete-time and continuous dynamical systems on the subset of a strongly ordered Banach space. Then we discuss cooperative systems of functional differential equations and further obtain a threshold theorem on their global asymptotic behavior under the sublinearity assumption. Finally, we give some application examples in epidemic and population dynamics. Some related earlier results are generalized and improved.