Chaos and control of a three-dimensional fractional order discrete-time system with no equilibrium and its synchronization
Source abstract
Abstract
Chaotic systems with no equilibrium are a very important topic in nonlinear dynamics. In this paper, a new fractional order discrete-time system with no equilibrium is proposed, and the complex dynamical behaviors of such a system are discussed numerically by means of a bifurcation diagram, the largest Lyapunov exponents, a phase portrait, and a 0–1 test. In addition, a one-dimensional controller is proposed. The asymptotic convergence of the proposed controller is established by means of the stability theory of linear fractional order discrete-time systems. Next, a synchronization control scheme for two different fractional order discrete-time systems with hidden attractors is reported, where the master system is a two-dimensional system that has been reported in the literature. Numerical results are presented to confirm the results.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Chaos control and synchronization · Nonlinear Dynamics and Pattern Formation · stochastic dynamics and bifurcation
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi 1 , Tebessa 12002 Algeria
Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University 2 , P.O. Box: 346 Ajman, United Arab Emirates
Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi 3 , Oum El Bouaghi 04000, Algeria
Department of Mathematics, Faculty of Science, University of Jordan 4 , Amman 11942, Jordan
Universita del Salento, Dipartimento Ingegneria Innovazione 5 , 73100 Lecce, Italy
Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University 6 , Ho Chi Minh City 700000, Vietnam
References (28)
Show source-provided references
1. 2015
2. 2015
3. Discrete chaos in fractional delayed logistic maps10.1007/s11071-014-1250-3 ↗
4. On chaos in the fractional-order grassi–miller map and its control10.1016/j.cam.2019.03.031 ↗
5. On the dynamics and control of a fractional form of the discrete double scroll10.1142/s0218127419500780 ↗
6. On the dynamics, control and synchronization of fractional-order Ikeda map10.1016/j.chaos.2019.04.002 ↗
7. On fractional–order discrete–time systems: Chaos, stabilization and synchronization10.1016/j.chaos.2018.12.019 ↗
8. The fractional form of a new three-dimensional generalized Hénon map10.1186/s13662-019-2064-x ↗
9. On chaos in the fractional-order discrete-time unified system and its control synchronization10.3390/e20070530 ↗
10. A new contribution for the impulsive synchronization of fractional–order discrete–time chaotic systems10.1007/s11071-017-3743-3 ↗
11. On the Q–S chaos synchronization of fractional-order discrete-time systems: General method and examples10.1155/2018/2950357 ↗
12. The co-existence of different synchronization types in fractional-order discrete-time chaotic systems with non–identical dimensions and orders10.3390/e20090710 ↗
13. Generalized and inverse generalized synchronization of fractional-order discrete-time chaotic systems with non-identical dimensions10.1186/s13662-018-1764-y ↗
14. Synchronisation of integer-order and fractional-order discrete-time chaotic systems10.1007/s12043-018-1712-0 ↗
15. Chaos synchronization of fractional–order discrete–time systems with different dimensions using two scaling matrices10.1515/phys-2019-0099 ↗
16. Hidden attractors in dynamical systems: From hidden oscillation in Hilbert-Kolmogorov, Aizerman and Kalman problems to hidden chaotic attractor in Chua circuits10.1142/s0218127413300024 ↗
17. Hidden attractors in dynamical models of phase-locked loop circuits: Limitations of simulation in MATLAB and SPICE10.1016/j.cnsns.2017.03.010 ↗
18. Hidden chaotic attractors in a class of two–dimensional maps10.1007/s11071-016-2857-3 ↗
19. A new class of three-dimensional maps with hidden chaotic dynamics10.1142/s0218127416502060 ↗
20. A new two–dimensional map with hidden attractors10.3390/e20050322 ↗
21. Chaotic map with no fixed points: Entropy, implementation and control10.3390/e21030279 ↗
22. On Riemann and Caputo fractional differences10.1016/j.camwa.2011.03.036 ↗
23. Discrete fractional calculus with the nabla operator10.14232/ejqtde.2009.4.3 ↗
24. Principles of delta fractional calculus on time scales and inequalities10.1016/j.mcm.2010.03.055 ↗
25. Jacobian matrix algorithm for Lyapunov exponents of the discrete fractional maps10.1016/j.cnsns.2014.06.042 ↗
26. On the implementation of the 0–1 test for chaos10.1137/080718851 ↗
27. On explicit stability condition for a linear fractional difference system10.1515/fca-2015-0040 ↗
28. Fractional form of a chaotic map without fixed points: Chaos, entropy and control10.3390/e20100720 ↗