Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation
Abstract
:1. Introduction
1.1. Motivation and Literature Review
1.2. Structure of the Paper
2. Main Results
Dynamics of
- (1)
- necessary condition.
- (2)
- sufficient condition.
- (i)
- (ii)
- (i)
- (ii)
- (iii)
3. Existence of Neimark-Sacker Bifurcation of
Direction of Neimark–Sacker Bifurcation
4. Numerical Simulation
5. Conclusions and Findings
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Khaliq, A.; Mustafa, I.; Ibrahim, T.F.; Osman, W.M.; Al-Sinan, B.R.; Dawood, A.A.; Juma, M.Y. Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation. Fractal Fract. 2023, 7, 113. https://doi.org/10.3390/fractalfract7020113
Khaliq A, Mustafa I, Ibrahim TF, Osman WM, Al-Sinan BR, Dawood AA, Juma MY. Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation. Fractal and Fractional. 2023; 7(2):113. https://doi.org/10.3390/fractalfract7020113
Chicago/Turabian StyleKhaliq, Abdul, Irfan Mustafa, Tarek F. Ibrahim, Waleed M. Osman, Bushra R. Al-Sinan, Arafa Abdalrhim Dawood, and Manal Yagoub Juma. 2023. "Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation" Fractal and Fractional 7, no. 2: 113. https://doi.org/10.3390/fractalfract7020113