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ISSN : 1226-0657

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Vol.15 No.3
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Hopf Bifurcation Properties of Holling Type Predator-prey Systems

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2008, v.15 no.3, pp.329-342
Shin, Seong-A
Shin,, S. (2008). Hopf Bifurcation Properties of Holling Type Predator-prey Systems. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 15(3), 329-342.
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Abstract

There have been many experimental and observational evidences which indicate the predator response to prey density needs not always monotone increasing as in the classical predator-prey models in population dynamics. Holling type functional response depicts situations in which sufficiently large number of the prey species increases their ability to defend or disguise themselves from the predator. In this paper we investigated the stability and instability property for a Holling type predator-prey system of a generalized form. Hopf type bifurcation properties of the non-diffusive system and the diffusion effects on instability and bifurcation values are studied.

keywords
predator-prey system, diffusion pressures, Holling-type functional responses, asymptotic behaviors, Hopf type bifurcation, kinetic system, diffusive instability

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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