Dynamical analysis of discretized Logistic model with Caputo- Fabrizio fractional derivative
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 s...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
International Academy of Ecology and Environmental Sciences
2021-03-01
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| Series: | Computational Ecology and Software |
| Subjects: | |
| Online Access: | http://www.iaees.org/publications/journals/ces/articles/2021-11(1)/dynamical-analysis-of-discretized-Logistic-model.pdf |
| Summary: | 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.
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| ISSN: | 2220-721X 2220-721X |