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Existence and global stability of positive periodic solution of periodic integro-differential systems with feedback controls. (English) Zbl 0962.45003

The purpose of this paper is to derive a set of sufficient conditions for the existence and global asymptotic stability of a positive periodic solution of some periodic integro-differential systems with feedback controls, applied to describe the temporal evolution of \(n\) competitive species population in a common environment, by using the technique of coincidence degree theory and Lyapunov functionals.

MSC:

45M05 Asymptotics of solutions to integral equations
92D25 Population dynamics (general)
45J05 Integro-ordinary differential equations
45M20 Positive solutions of integral equations
34K50 Stochastic functional-differential equations
93B52 Feedback control
45M10 Stability theory for integral equations
45M15 Periodic solutions of integral equations
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