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

作者：Ongun Mevlude Yakit^*; Ozdogan Nihal

来源：Journal of Nonlinear Sciences and Applications, 2017, 10(2): 713-723.

DOI：10.22436/jnsa.010.02.32

• Allee effect
• stability analysis
• nonstandard finite difference scheme
• predator-prey model

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.

• 出版日期2017