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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.15 No.3

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HOPF BIFURCATION PROPERTIES OF HOLLING TYPE PREDATOR-PREY SYSTEMS

Hopf Bifurcation Properties of Holling Type Predator-prey Systems

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2008, v.15 no.3, pp.329-342
Shin, Seong-A (Department of Mathematics, Sungshin Women's University)
Shin, Seong-A. (2008). HOPF BIFURCATION PROPERTIES OF HOLLING TYPE PREDATOR-PREY SYSTEMS, 15(3), 329-342.

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

한국수학교육학회지시리즈B:순수및응용수학

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