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STABILITY ANALYSIS OF A LOTKA–VOLTERRA TYPE PREDATOR–PREY SYSTEM INVOLVING ALLEE EFFECTS

Part of: Stability theory General theory in ordinary differential equations

Published online by Cambridge University Press:  03 August 2011

HÜSEYİN MERDAN
HÜSEYİN MERDAN*
Affiliation:
TOBB University of Economics and Technology, Faculty of Arts and Sciences, Department of Mathematics, Söğütözü 06530, Ankara, Turkey (email: merdan@etu.edu.tr)
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Abstract

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We present a stability analysis of steady-state solutions of a continuous-time predator–prey population dynamics model subject to Allee effects on the prey population which occur at low population density. Numerical simulations show that the system subject to an Allee effect takes a much longer time to reach its stable steady-state solution. This result differs from that obtained for the discrete-time version of the same model.

Keywords

Allee effectspopulation dynamicsstability analysispredator–prey model

MSC classification

Secondary: 34D20: Stability 34A34: Nonlinear equations and systems, general
Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 2 , October 2010 , pp. 139 - 145
Copyright
Copyright © Australian Mathematical Society 2011

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