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Computational Ecology and Software, 2021, 11(1): 21-34
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Article

Dynamical analysis of discretized Logistic model with Caputo- Fabrizio fractional derivative

H. Karakaya¹, I. Ozturk¹, S. Kartal², F. Gurcan³
¹Erciyes University, Kayseri, Turkey
²Nevsehir Haci Bektas Veli University, Nevsehir, Turkey
³Kuwait University, Safat, Kuwait

Received 29 August 2020;Accepted 10 October 2020;Published 1 March 2021
IAEES

Abstract
In this paper we consider a fractional order Logistic model with Caputo-Fabrizio fractional derivative. By applying two-step Adams-Bashforth scheme, we obtain a system of difference equations. By using the Schur-Cohn criterion, stability conditions of the positive equilibrium point of the discrete system are obtained. It is observed that the discrete system shows much richer dynamic behaviors than its fractional-order form such as Neimark-Sacker bifurcation and chaos. The direction and stability of the Neimark-Sacker bifurcation are determined by using the normal form and center manifold theory. In addition, the effect of fractional order parameter on the dynamical behavior of the system is investigated. Finally, numerical simulations are used to demonstrate the accuracy of analytical results.

Keywords Caputo-Fabrizio fractional derivative;two-step Adams-Basforth Method;Logistic differential equation;Neimark-Sacker bifurcation.

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