A nonstandard numerical scheme for a predator-prey model with Allee effect


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.


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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


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