Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay

Xuepeng Li and Wensheng Yang

Abstract and Applied Analysis, 2009, vol. 2009, 1-6

Abstract:

Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay ̇ ð ‘¥ 1 ( ð ‘¡ ) = ð ‘¥ 1 ( ð ‘¡ ) [ ð ‘Ÿ 1 ( ð ‘¡ ) − ð ‘Ž 1 1 ( ð ‘¡ ) ð ‘¥ 1 ( ð ‘¡ − ð œ ( ð ‘¡ ) ) − ð ‘Ž 1 2 ( ð ‘¡ ) ð ‘¥ 2 ( ð ‘¡ ) / ( ð ‘š 2 + ð ‘¥ 2 1 ( ð ‘¡ ) ) ] , ̇ ð ‘¥ 2 ( ð ‘¡ ) = ð ‘¥ 2 ( ð ‘¡ ) [ ð ‘Ÿ 2 ( ð ‘¡ ) − ð ‘Ž 2 1 ( ð ‘¡ ) ð ‘¥ 2 ( ð ‘¡ ) / ð ‘¥ 1 ( ð ‘¡ ) ] , are obtained, where ð ‘¥ 1 ( ð ‘¡ ) and ð ‘¥ 2 ( ð ‘¡ ) stand for the density of the prey and the predator, respectively, and ð ‘š ≠0 is a constant. ð œ ( ð ‘¡ ) ≥ 0 stands for the time delays due to negative feedback of the prey population.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:960823

DOI: 10.1155/2009/960823

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