Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional Response

Guohong Zhang and Xiaoli Wang

Abstract and Applied Analysis, 2011, vol. 2011, 1-16

Abstract:

We study a general Gause-type predator-prey model with monotonic functional response under Dirichlet boundary condition. Necessary and sufficient conditions for the existence and nonexistence of positive solutions for this system are obtained by means of the fixed point index theory. In addition, the local and global bifurcations from a semitrivial state are also investigated on the basis of bifurcation theory. The results indicate diffusion, and functional response does help to create stationary pattern.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:547060

DOI: 10.1155/2011/547060

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