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Stability Analysis of Equilibrium Manifolds for a Two-Predators One-Prey Model

Xin ZHANG, Yun TANG( ), Rudolf Scherer†
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Institute of Practical Mathematics, University of Karlsruhe, D-76128 Karlsruhe, Germany
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Abstract

The objective of this paper is to analyze the stability of equilibrium manifolds for a ratio-dependent two-predators one-prey model. Some model results are presented first with the bifurcation without parameters method, and then the method was used to study bifurcation along the equilibrium manifold for the model. The model does not lose stability even when some equilibria are locally unstable because the equilibrium manifold is stable when treated as a whole. The ecological implications of the results are discussed.

Keywords

bifurcationequilibrium manifoldpredator-prey modelstability

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Tsinghua Science and Technology
Volume 11 Issue 6,
December 2006
Pages 739-744
DOI: 10.1016/S1007-0214(06)70258-9

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Cite this article:
ZHANG X, TANG Y, Scherer R. Stability Analysis of Equilibrium Manifolds for a Two-Predators One-Prey Model. Tsinghua Science and Technology, 2006, 11(6): 739-744. https://doi.org/10.1016/S1007-0214(06)70258-9

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Received: 18 March 2005
Published: 01 December 2006
© Tsinghua University Press 2006