Global asymptotic properties for a Leslie-Gower food chain model

Andrei Korobeinikov; William T. Lee

doi:10.3934/mbe.2009.6.585

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2009, Volume 6, Issue 3: 585-590. Doi: 10.3934/mbe.2009.6.585

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Global asymptotic properties for a Leslie-Gower food chain model

Andrei Korobeinikov^1, and
William T. Lee^1,

1.
MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick

Received: June 30, 2008

Revised: September 30, 2008

Published: May 2009

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Abstract

We study global asymptotic properties of a continuous time Leslie-Gower food chain model. We construct a Lyapunov function which enables us to establish global asymptotic stability of the unique coexisting equilibrium state.

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Mathematics Subject Classification: Primary: 92D30; Secondary: 34D20.

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