On a diffusive predator-prey model with nonlinear harvesting

Peng Feng

doi:10.3934/mbe.2014.11.807

Article Contents

2014, Volume 11, Issue 4: 807-821. Doi: 10.3934/mbe.2014.11.807

This issue Previous Article Stability and bifurcation analysis of epidemic models with saturated incidence rates: An application to a nonmonotone incidence rate Next Article Coexistence and asymptotic stability in stage-structured predator-prey models

On a diffusive predator-prey model with nonlinear harvesting

Peng Feng^1,

1.
Department of Mathematics, Florida Gulf Coast University, 11501 FGCU Blvd. S., Fort Myers, FL 33965

Received: August 2013

Revised: November 2013

Published: February 2014

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Abstract

In this paper, we study the dynamics of a diffusive Leslie-Gower model with a nonlinear harvesting term on the prey. We analyze the existence of positive equilibria and their dynamical behaviors. In particular, we consider the model with a weak harvesting term and find the conditions for the local and global asymptotic stability of the interior equilibrium. The global stability is established by considering a proper Lyapunov function. In contrast, the model with strong harvesting term has two interior equilibria and bi-stability may occur for this system. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

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Mathematics Subject Classification: Primary: 35K40, 35K57, 35B36; Secondary: 35Q92.

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