Global stability analysis of a ratio-dependent predator-prey system

doi:10.1007/s10483-008-0407-y

Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (4): 495-500 .doi: https://doi.org/10.1007/s10483-008-0407-y

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Global stability analysis of a ratio-dependent predator-prey system

LU Tie-jun, WANG Mei-juan, LIU Yan

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China

Received:2007-04-12 Revised:2008-01-16 Online:2008-04-18 Published:2008-04-18
Contact: WANG Mei-juan

Abstract

Abstract: A ratio dependent predator-prey system with Holling type III functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymptotic stability of the positive equilibrium. The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.

Key words: Hopf bifurcation, ratio-dependent, global asymptotic stability, functional response

2010 MSC Number:

LU Tie-jun;WANG Mei-juan;LIU Yan. Global stability analysis of a ratio-dependent predator-prey system. Applied Mathematics and Mechanics (English Edition), 2008, 29(4): 495-500 .

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Global stability analysis of a ratio-dependent predator-prey system

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