Global dynamics in the leslie-gower model with the allee effect

Valery A. Gaiko; Cornelis Vuik

doi:10.1142/S0218127418501511

Global dynamics in the leslie-gower model with the allee effect

Valery A. Gaiko, Cornelis Vuik

Numerical Analysis

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12 Citations (Scopus)

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Abstract

We complete the global bifurcation analysis of the Leslie-Gower system with the Allee effect which models the dynamics of the populations of predators and their prey in a given ecological or biomedical system. In particular, studying global bifurcations of limit cycles, we prove that such a system can have at most two limit cycles surrounding one singular point.

Original language	English
Article number	1850151
Pages (from-to)	1-10
Number of pages	10
Journal	International Journal of Bifurcation and Chaos
Volume	28
Issue number	12
DOIs	https://doi.org/10.1142/S0218127418501511
Publication status	Published - 2018

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Allee effect
bifurcation
field rotation parameter
Leslie-Gower model
limit cycle
singular point
Wintner-Perko Termination Principle

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Global dynamics in the leslie-gower model with the allee effect

Abstract

Bibliographical note

Keywords

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