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Existence and global stability of periodic solutions of a discrete ratio-dependent food chain model with delay. (English) Zbl 1073.93050

A discrete ratio-dependent food chain model with delays is considered. Sufficient conditions for the global existence of positive periodic solutions are derived. These conditions ar similar to those for the corresponding continuous system. By means of constructing a suitable Lyapunov function, sufficient conditions for the global stability of positive periodic solutions are also obtained. The problems considered are associated with the study of a multispecies population interaction in a periodic environment.

MSC:

93D20 Asymptotic stability in control theory
93C55 Discrete-time control/observation systems
92D25 Population dynamics (general)
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