IJPAM: Volume 115, No. 2 (2017)

Title

DYNAMICS OF LESLIE-GOWER PREDATOR-PREY
MODEL WITH ADDITIONAL FOOD FOR PREDATORS

Authors

Hana Maria Ulfa$^1$, Agus Suryanto$^2$, Isnani Darti$^3$
$^{1,2,3}$Departement of Mathematics
Brawijaya University
Jl. Veteran Malang 65145, INDONESIA

Abstract

We consider a Leslie-Gower predator prey model with additional food for predators. Here we investigate the dynamics of the model such as the permanence, determination of equilibrium points and their existence condition as well as their stability properties. It is shown that the model is permanence and has four equilibrium points, i.e., the extinction of both prey and predator point, the extinction of prey point, the extinction of predator and the coexistence point. The point of prey extinction and the coexistence point are conditionally stable while two other equilibrium points are always unstable. It is also shown that the additional food for predators may destabilize the extinction of prey point and at the same time stabilize the coexistence point. Such dynamical behavior agrees with our numerical results.

History

Received: July 11, 2016
Revised: April 5, 2017
Published: July 14, 2017

AMS Classification, Key Words

AMS Subject Classification: 34C60, 92D40
Key Words and Phrases: predator-prey model, Leslie-Gower model, permanence, additional food

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How to Cite?

DOI: 10.12732/ijpam.v115i2.1 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 2
Pages: 199 - 209


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