Positive periodic solutions for a generalized two-species semi-ratio-dependent predator-prey system in a two-patch environment

Authors:
Xiaoquan Ding;Jifa Jiang
Affiliations:
Department of Mathematics, Tongji University, Shanghai 200092, PR China and Department of Mathematics and Information Science, Shandong Agricultural University, Tai'an, Shandong 271018, PR China;Department of Mathematics, Shanghai Normal University, Shanghai 200234, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

Citing 4
Cited 0

Global stability for a class of predator-prey systems

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Global analyses in some delayed ratio-dependent predator-prey systems

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Global asymptotic stability of a predator-prey system of Holling type

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Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response

Mathematical and Computer Modelling: An International Journal

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Abstract

In this paper, we investigate a generalized two-species semi-ratio-dependent predator-prey system with the prey dispersal in a two-patch environment. With the help of a continuation theorem based on coincidence degree theory, we establish sufficient conditions for the existence of positive periodic solutions. Our results show that for any monotonic prey growth and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod-Haldane type, and the Beddington-DeAngelis type, the system always has at least one positive periodic solution.