A nonstandard numerical scheme for a predator-prey model with Allee effect
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Authors
Mevlude Yakit Ongun
- Department of Mathematics, Suleyman Demirel University, Isparta, Turkey.
Nihal Ozdogan
- Vocational School of Higher Education, Suleyman Demirel University, Isparta, Turkey.
Abstract
In this paper, we present a Lotka-Volterra predator-prey model with Allee effect. This system with general functional
response has an Allee effect on prey population. A nonstandard finite difference scheme is constructed to transform the continuous
time predator-prey model with Allee effect into the discrete time model. We use the Schur-Cohn criteria which deal
with coefficients of the characteristic polynomial for determining the stability of discrete time system. The proposed numerical
schemes preserve the positivity of the solutions with positive initial conditions. The new discrete-time model shows dynamic
consistency with continuous-time model.
Share and Cite
ISRP Style
Mevlude Yakit Ongun, Nihal Ozdogan, A nonstandard numerical scheme for a predator-prey model with Allee effect, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 713--723
AMA Style
Ongun Mevlude Yakit, Ozdogan Nihal, A nonstandard numerical scheme for a predator-prey model with Allee effect. J. Nonlinear Sci. Appl. (2017); 10(2):713--723
Chicago/Turabian Style
Ongun, Mevlude Yakit, Ozdogan, Nihal. "A nonstandard numerical scheme for a predator-prey model with Allee effect." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 713--723
Keywords
- Allee effect
- stability analysis
- nonstandard finite difference scheme
- predator-prey model.
MSC
References
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