IJPAM: Volume 105, No. 2 (2015)

STABILITY ANALYSIS OF THE EULER DISCRETIZATION
FOR THE HARVESTING LESLIE-GOWER
PREDATOR-PREY MODEL

Prisca Danik Ernawati$^1$, Isnani Darti$^2$
$^{1,2}$Department of Mathematics
Brawijaya University
Jl. Veteran Malang, 65145, INDONESIA


Abstract. In this paper, a harvesting Leslie-Gower equations is discretized using the forward Euler method. The dynamical properties of the resulted discrete system is then analysed. It is shown that the discrete system has exactly the same equilibria as those of original continuous equation. However, the stability of positive equilibrium is dynamically consistent with its continuous version only for relatively small time step. Such behaviour is confirmed by our numerical simulations. Furthermore, our numerical simulations show when the time step does not satisfy the stability condition, the discrete system has more complicated dynamics such as period-$2^n$-orbits and chaos.

Received: September 1, 2015

AMS Subject Classification: 37N25, 92D40

Key Words and Phrases: difference equation, forward Euler method, dynamically consistent, asymptotically stable

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DOI: 10.12732/ijpam.v105i2.8 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: 2015
Volume: 105
Issue: 2
Pages: 213 - 221


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