‎S‎ynchronization ‎of‎ different ‎dimensions‎ ‎fractional-‎order chaotic ‎systems with uncertain‎‎ ‎ parameters ‎and ‎secure ‎communication‎‎‎‎‎
DOI:
https://doi.org/10.5269/bspm.41252Abstract
In ‎this ‎paper, ‎an‎ adaptive ‎modified‎ function projective synchronization (‎AM‎FPS) ‎scheme‎ ‎of ‎different ‎dimensions‎‎ ‎fractional-‎order ‎chaotic systems with ‎fully ‎unknown parameters is ‎presented‎. ‎On the basis of ‎fractional‎ Lyapunov stability ‎theory ‎and adaptive control law‎,‎ a‎ ‎new‎ fractional-order controller ‎and‎ suitable ‎‎‎‎update ‎rules‎ for unknown parameters are ‎designed‎‎ to realize the ‎AMFPS‎ of different ‎fractional-‎order chaotic systems with ‎non-‎identical ‎orders ‎and different dimensions‎‎. ‎‎Theoretical analysis and numerical simulations are given to verify the validity ‎of ‎the proposed ‎method. ‎Additionally, ‎‎‎‎synchronization results ‎are applied to secure communication via ‎‎ ‎modified ‎‎‎‎masking ‎method. Due to the unpredictability of the scale ‎function ‎matrix‎ and ‎using‎ of ‎fractional-‎order ‎systems with different ‎dimensions ‎and ‎u‎nequal‎ ‎orders,‎‎ the proposed scheme has higher ‎security‎‎. The security analysis ‎‎‎demonstrate that the proposed algorithm ‎has ‎a large key space ‎and‎ high sensitivity to encryption keys ‎and it is ‎‎re‎sistance to all kind of ‎‎attacks‎.
References
2. D. Wei, X. Wang, J. Hou and P. Liu, Hybrid projective synchronization of complex Duffing-Holmes oscillators with application to image encryption, Math. Meth. Appl. Sci., 40(12), 4259-4271, (2017). DOI: 10.1002/mma.4302.
3. X. Wu, Y. Li and J. Kurths, A new color image encryption scheme using CML and a fractional-order chaotic system, PLOS ONE, 10(3), 1-28, (2015). DOI:10.1371/journal.pone.0119660
4. S. K. Agrawal and S. Das, Projective synchronization between different fractional-order hyperchaotic systems with uncertain parameters using proposed modified adaptive projective synchronization technique, Math. Meth. Appl. Sci., 37(14), 2164-2176, (2014). DOI: 10.1002/mma.2963.
5. H. Liang, Z. Wang, Z. Yue and R. Lu, Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication, Kybernetika, 48(2), 190-205, (2012).
6. C. Feng, X. Lei and L. Chun-Guang, Wavelet Phase Synchronization of fractional- order Chaotic Systems, CHIN. PHYS. LETT., 29(7), 070501, (2012). DOI:10.1088/0256-307X/29/7/070501
7. Y. Xu, H. Wang, D. Liu and H. Huang, Sliding mode control of a class of fractional chaotic systems in the presence of parameter perturbations, J. Vib. Control, 21(3), 435-448, (2015). DOI:10.1177/1077546313486283.
8. R. Mainieri and J. Rehacek, Projective synchronization in three dimensional chaotic systems, Phys. Rev. Lett., 82(15), 3042-3045, (1999).
9. G. H. Li, Modified projective synchronization of chaotic system, Chaos Solitons Fractals, 32(5), 1786-1790, (2007). DOI:10.1016/j.chaos.2005.12.009
10. Y. Chen and X. Li, Function projective synchronization between two identical chaotic systems, Internat. J. Modern Phys. C, 18(5), 883-888, (2007). DOI:10.1142/S0129183107010607
11. H. Y. Du, Q. S. Zeng and C.H. Wang, Modified function projective synchronization of chaotic system, Chaos Solitons Fractals, 42(4), 2399-2404, (2009). DOI:10.1016/j.chaos.2009.03.120
12. H. T. Yau, Y. C. Pu and S. C. Li, Application of a Chaotic Synchronization System to Secure Communication, Inf. Technol. control, 41(3), 274-282, (2012). DOI:10.5755/j01.itc.41.3.1137
13. M. Caputo, Linear models of dissipation whose Q is almost frequency independent-II, Geophys J. R. Astron. Soc., 13(5), 529-539, (1967). DOI:10.1111/j.1365-246X.1967.tb02303.x.
14. Y. Li, Y. Chen and I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag Leffler stability Comput Math Appl., 59(5), 1810-1821, (2010). DOI:10.1016/j.camwa.2009.08.019.
15. M. A. Duarte-Mermoud, N. Aguila-Camacho, J.A. Gallegos and R. Castro-Linares, Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems, Commun. Nonlinear Sci. Numer. Simul., 22(1), 650-659, (2015). DOI:10.1016/j.cnsns.2014.10.008
16. J. J. Slotine and W. Li, Applied nonlinear control, Prentice Hall, (1991).
17. K. Diethelm, N. Ford and A. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynam., 29(1), 3-22, (2002). DOI:10.1023/A:1016592219341
18. C. G. Li and G. R. Chen, Chaos in the fractional order Chen system and its control, Chaos Solitons Fractals, 22(3), 549-554, (2004). DOI:10.1016/j.chaos.2004.02.035
19. X. Wu and Y. Lu, Generalized projective synchronization of the fractional-order Chen hyperchaotic system, Nonlinear Dynam, 57(1), 25-35, (2009). DOI:10.1007/s11071-008-9416-5
20. D. R. Stinson, Cryptography: Theory and Practice, Boca Raton, CRC Press, (2005).
21. C. E. Shannon, Communication Theory of Secrecy Systems, Bell Syst. Tech. J., 28(4), 656-715, (1949). DOI:10.1002/j.1538-7305.1949.tb00928.x
22. N. K. Pareek, Design and analysis of a novel digital image encryption schem, Internat. J. Netw. Secur. Appl., 4(2), 95-108, (2012). DOI: 10.5121/ijnsa.2012.4207
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