Comparative Analysis of the Chaotic Behavior of a Five-Dimensional Fractional Hyperchaotic System with Constant and Variable Order
Abstract
:1. Introduction
- 5D constant-order fractional Caputo hyperchaotic system:
- 5D variable-order fractional Caputo hyperchaotic system:
- 5D constant-order fractional Caputo–Fabrizio hyperchaotic system:
- 5D variable-order fractional Caputo–Fabrizio hyperchaotic system:
2. Preliminaries
3. Computational Techniques for Solving a 5D Constant- and Variable-Order Fractional Caputo Hyperchaotic System
3.1. Computational Techniques for Solving a 5D Constant-Order Caputo Hyperchaotic System
3.2. Computational Techniques for Solving a 5D Variable-Order Fractional Caputo Hyperchaotic System
4. Computational Techniques for Solving the 5D Constant- and Variable-Order Fractional CF Hyperchaotic Systems
4.1. Numerical Solutions for Solving the 5D Constant-Order Fractional CF Hyperchaotic System
4.2. A Computational Method for Solving the 5D Variable-Order Fractional CF Hyperchaotic System
4.3. Simulations
4.4. Discussion
- In Figure 1, the phase portraits illustrating the behavior of the 5D constant- and variable-order fractional hyperchaotic systems with the Caputo derivative are presented.
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Alqahtani, A.M.; Chaudhary, A.; Dubey, R.S.; Sharma, S. Comparative Analysis of the Chaotic Behavior of a Five-Dimensional Fractional Hyperchaotic System with Constant and Variable Order. Fractal Fract. 2024, 8, 421. https://doi.org/10.3390/fractalfract8070421
Alqahtani AM, Chaudhary A, Dubey RS, Sharma S. Comparative Analysis of the Chaotic Behavior of a Five-Dimensional Fractional Hyperchaotic System with Constant and Variable Order. Fractal and Fractional. 2024; 8(7):421. https://doi.org/10.3390/fractalfract8070421
Chicago/Turabian StyleAlqahtani, Awatif Muflih, Arun Chaudhary, Ravi Shanker Dubey, and Shivani Sharma. 2024. "Comparative Analysis of the Chaotic Behavior of a Five-Dimensional Fractional Hyperchaotic System with Constant and Variable Order" Fractal and Fractional 8, no. 7: 421. https://doi.org/10.3390/fractalfract8070421
APA StyleAlqahtani, A. M., Chaudhary, A., Dubey, R. S., & Sharma, S. (2024). Comparative Analysis of the Chaotic Behavior of a Five-Dimensional Fractional Hyperchaotic System with Constant and Variable Order. Fractal and Fractional, 8(7), 421. https://doi.org/10.3390/fractalfract8070421