journal article·2018-09-27Open access

Secure Multiple-Input Multiple-Output Communications Based on F–M Synchronization of Fractional-Order Chaotic Systems with Non-Identical Dimensions and Orders

Adel Ouannas, Nadjette Debbouche, Xiong Wang, Viet-Thanh Pham, Okba Zehrour

Applied Sciences· Volume 8· Issue 10

Abstract

This paper investigates the F – M synchronization between non-identical fractional-order systems characterized by different dimensions and different orders. F – M synchronization combines the inverse generalized synchronization with the matrix projective synchronization. In particular, the proposed approach enables the F – M synchronization to be achieved between an n-dimensional master system and an m-dimensional slave system. The developed approach is applied to chaotic and hyperchaotic fractional systems with the aim of illustrating its applicability and suitability. A multiple-input multiple-output (MIMO) secure communication system is also developed by using the F – M synchronization and verified through computer simulations.
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Research context

OpenAlex topics: Chaos control and synchronization · Chaos-based Image/Signal Encryption · Nonlinear Dynamics and Pattern Formation

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, Algeria

Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria

Institute for Advanced Study, Shenzhen University, Shenzhen 518060, Guangdong, China

Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Funding

National Natural Science Foundation of China · Shenzhen Overseas High Level Talent Peacock Project Fund

References (31)

Show source-provided references
1. A theory for synchronization of dynamical systems10.1016/j.cnsns.2008.07.002 ↗
2. Martinez-Guerra, R., Pérez-Pinacho, C.A., and Gómez-Cortés, G.C. (2015). Synchronization of Integral and Fractional Order Chaotic Systems, Springer.10.1007/978-3-319-15284-4 ↗
3. Inverse full state hybrid projective synchronization for chaotic maps with different dimensions10.1088/1674-1056/25/9/090503 ↗
4. On matrix projective synchronization and inverse matrix projective synchronization for different and identical dimensional discrete-time chaotic systems
5. Generalized synchronization of different dimensional chaotic dynamical systems in discrete-time10.1007/s11071-015-2026-0 ↗
6. On inverse generalized synchronization of continuous chaotic dynamical systems10.1007/s40819-015-0040-z ↗
7. A new approach to study the coexistence of some synchronization types between chaotic maps with different dimensions10.1007/s11071-016-2966-z ↗
8. A new approach to synchronize different dimensional chaotic maps using two scaling matrices
9. A robust control method for Q-S synchronization between different dimensional integer-order and fractional-order chaotic systems10.1155/2015/703753 ↗
10. Increased and reduced order synchronization of 2D and 3D dynamical systems
11. Increased-order generalized synchronization of chaotic and hyperchaotic systems10.1007/s12043-014-0835-1 ↗
12. Azar, A.T., Vaidyanathan, S., and Ouannas, A. (2017). Fractional Order Control and Synchronization of Chaotic Systems, Springer. Studies in Computational Intelligence.10.1007/978-3-319-50249-6 ↗
13. Chaos synchronization in fractional differential systems10.1098/rsta.2012.0155 ↗
14. Fractional chaos synchronization schemes for different dimensional systems with non-identical fractional-orders via two scaling matrices10.1016/j.ijleo.2016.06.006 ↗
15. On a function projective synchronization scheme for non-identical Fractional-order chaotic (hyperchaotic) systems with different dimensions and orders10.1016/j.ijleo.2017.02.068 ↗
16. Some basic cryptographic requirements for chaos based cryptosystems10.1142/S0218127406015970 ↗
17. Paar, C., and Pelzl, J. (2010). Understanding Cryptography, Springer.10.1007/978-3-642-04101-3 ↗
18. Kocarev, L., and Lian, S. (2011). Chaos-Based Cryptography: Theory, Algorithms and Applications, Springer.10.1007/978-3-642-20542-2 ↗
19. Miller, K.S., and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons.
20. Linear models of dissipation whose Q is almost frequency independent—II10.1111/j.1365-246X.1967.tb02303.x ↗
21. Podlubny, I., and Samko, S.G. (1999). Fractional Differential Equations, Academic Press. Mathematics in Science and Engineering.
22. Samko, S.G., Kilbas, A.A., and Marichev, O.I. (1993). Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach.
23. Efficient modified Chebyshev differentiation matrices for fractional differential equations10.1016/j.cnsns.2017.02.009 ↗
24. Comments on “Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks”10.1016/j.cnsns.2015.01.013 ↗
25. Analysis of fractional differential equations10.1006/jmaa.2000.7194 ↗
26. Detailed error analysis for a fractional Adams method10.1023/B:NUMA.0000027736.85078.be ↗
27. Chaotic behavior and circuit implementation of a fractional-order permanent magnet synchronous motor model10.1016/j.jfranklin.2015.05.025 ↗
28. Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication10.1016/j.nonrwa.2011.11.008 ↗
29. The generation and circuit implementation of a new hyper-chaos based upon Lorenz system10.1016/j.physleta.2006.09.042 ↗
30. Performance analysis of correlation-based communication schemes utilizing chaos10.1109/81.899920 ↗
31. Performance of MIMO relay DCSK-CD systems over Nakagami fading channels10.1109/TCSI.2012.2215755 ↗