Qualitative analysis of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses

Jun Zhou

doi:10.3934/cpaa.2015.14.1127

Article Contents

2015, Volume 14, Issue 3: 1127-1145. Doi: 10.3934/cpaa.2015.14.1127

This issue Previous Article Klein-Gordon-Maxwell equations in high dimensions Next Article Steady-state solutions and stability for a cubic autocatalysis model

Qualitative analysis of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses

Jun Zhou^1,

1.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715

Received: March 31, 2014

Revised: December 31, 2014

Published: April 2015

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Abstract

In this paper, we study a modified Leslie-Gower predator-prey model with Crowley-Martin functional response. We show the existence of a bounded positive invariant attracting set and establish the permanence conditions. The parameter regions for the stability and instability of the unique constant steady state solution are derived, and the existence of time-periodic orbits and non-constant steady state solutions are proved by bifurcation method.

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Mathematics Subject Classification: Primary: 35B32, 35B50, 35J65, 35K57, 37C25; Secondary: 92D25.

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