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Dynamics of a nonautonomous predator–prey system with the Beddington-DeAngelis functional response. (English) Zbl 1051.34033
The authors study the dynamics of a nonautonomous predator-prey system with Beddington-DeAngelis functional response. They argue that this system is more realistic than the Holling type response. Then they derive sufficient conditions for the persistence and global stability of the system. Motivated by the observed environmental changes, they study the case when all the coefficients are periodic or almost periodic with a given period. They derive sufficient conditions for the existence of positive periodic solutions and of boundary periodic solutions (where the predator extincts). Similar results are obtained for the almost-periodic case. They performed numerical simulations which has indicated that some of their conditions can be relaxed. In the reviewer’s opinion this is a very impressive work.

MSC:
34C25 Periodic solutions to ordinary differential equations
92D25 Population dynamics (general)
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
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