The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 15 Issue 3
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- Pages.329-342
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- 2008
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
HOPF BIFURCATION PROPERTIES OF HOLLING TYPE PREDATOR-PREY SYSTEMS
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