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

ISSN : 1226-0657

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Vol.25 No.4

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PHASE ANALYSIS FOR THE PREDATOR-PREY SYSTEMS WITH PREY DENSITY DEPENDENT RESPONSE

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
2018, v.25 no.4, pp.345-355
https://doi.org/10.7468/jksmeb.2018.25.4.345
Chang, Jeongwook
Shim, Seong-A
Chang,, J. , & Shim,, S. (2018). PHASE ANALYSIS FOR THE PREDATOR-PREY SYSTEMS WITH PREY DENSITY DEPENDENT RESPONSE. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 25(4), 345-355, https://doi.org/10.7468/jksmeb.2018.25.4.345

Abstract

This paper looks into phase plane behavior of the solution near the positive steady-state for the system with prey density dependent response functions. The positive invariance and boundedness property of the solution to the objective model are proved. The existence result of a positive steady-state and asymptotic analysis near the positive constant equilibrium for the objective system are of interest. The results of phase plane analysis for the system are proved by observing the asymptotic properties of the solutions. Also some numerical analysis results for the behaviors of the solutions in time are provided.

keywords
phase plane, density dependent response, existence properties of a positive steady-state, asymptotic properties

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

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