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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.17 No.3

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STABILITY ANALYSIS FOR 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
2010, v.17 no.3, pp.211-229
Shim, Seong-A
Shim,, S. (2010). STABILITY ANALYSIS FOR PREDATOR-PREY SYSTEMS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(3), 211-229.

Abstract

Various types of predator-prey systems are studied in terms of the stabilities of their steady-states. Necessary conditions for the existences of non-negative constant steady-states for those systems are obtained. The linearized stabilities of the non-negative constant steady-states for the predator-prey system with monotone response functions are analyzed. The predator-prey system with non-monotone response functions are also investigated for the linearized stabilities of the positive constant steady-states.

keywords
the classical Lotka-Volterra predator-prey system, Holling type II, III, IV functional responses, non-negative constant steady-states, linear stabilities

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