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Global Chaos Synchronization of Identical and Nonidentical Chaotic Systems Using Only Two Nonlinear Controllers

Authors: ISRAR AHMAD, Azizan Bin Saaban, Adyda Binti Ibrahim, Mohammad Shehzad

Abstract:

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on Lyapunov stability theory and using non-linear active control algorithm, it has been shown that the proposed schemes have excellent transient performance using only two nonlinear controllers and have shown analytically as well as graphically that synchronization is asymptotically globally stable.

Keywords: Synchronization, Lyapunov stability theory, Nonlinear Active Control, Chen and Tigan Chaotic systems

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1089403

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References:


[1] E. Lorenz, "Deterministic nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, no. 2, 1963, pp. 130–141.
[2] L. Pecora and T. Carroll, Synchronization in Chaotic Systems. Phys. Rev. Lett. 64, 1990, pp.821– 823.
[3] Yan-Ni li, et al., .Experimental study of chaos synchronization in the Belousov– Zhabotinsky chemical system. Chaos, Solitons and Fractals, Vol. 22, issue.14, 2004, pp.767-771.
[4] A. N. Pisarchik, et al., Synchronization of Shilnikov Chaos in a CO2 Laser with feedback. Laser Physics, Vol. 11, No. 11, 2001, pp. 1235–1239.
[5] Olga Moskalenko, et al., Generalized synchronization of chaos for secure communication: remarkable stability to noise. Phys. Lett. A. 374, 2010, pp. 2925-2931.
[6] Y. Lei, et al., Synchronization of two chaotic nonlinear gyros using active control, Phy. Lett. A, 343, 2005, pp. 153-158
[7] M. G. Rosenblum et al., Synchronization approach to analysis of Biological systems. An Interdisciplinary Sci. Journal on Random Processes in Physical, Biological and Technological Systems, Vol. 4, Issue 01, 2004.
[8] M. Shahzad, Israr Ahmad. Experimental Study of Synchronization & Anti- synchronization for Spin Orbit Problem of Enceladus. International Journal of Control Science and Engineering, 3(2), 2013, pp. 41-47.
[9] Vaidyanathan. Adaptive Controller and Synchronization Design for Hyperchaotic Zhou Systems with unknown Parameters. IJITMC Vol.1, No.1 (2013).
[10] Hsien- keng Chen. Global chaos synchronization of new chaotic systems via non- linear control. Chaos, Solitons and Fractals 23, 2005, pp. 1245-1251.
[11] Daolin XU and Zhigang LI. Controlled Projective Synchronization in Nonpartially- Linear Chaotic systems. International Journal of Bifurcation and Chaos, Vol. 12, No. 6, 2002, pp. 1395-1402.
[12] E. Vincent. Chaos synchronization using Active control and Backsteeping Control. Nonlinear Any: Modelling & Control, Vol. 13, No. 2, 2008, pp. 253-261.
[13] G. P. Jiang, et al., A global synchronization criterion for coupled chaotic systems via unidirectional linear error state feedback approach. Int. J. Bifurcation Chaos, Vol. 12, No. 10, 2002, pp. 2239-2253.
[14] Mehmet Akbar, Umit Ozguner, Decenterilization Sliding Mode Control Design using overlapping decomposition. Autometica 38, 2002, pp. 1713-1718.
[15] V. Sundarapandian. Global Chaos Anti-Synchronization of Tigan and Lorenz by Nonlinear Control. International Journal of Mathematical Sciences and Applications, Vol. 1, No.2, 2011.
[16] V. Sundarapandian. Hybrid Synchronization of Liu and Chen systems by Active Nonlinear control. International Journal of Mathematical Sciences and Applications, Vol. 1, No.3, 2011.
[17] V.Sundarapandian. Hybrid Synchronization of Liu-Chen and Tigan systems by Active Nonlinear Control. International Journal of Advances in Science and Technology, Vol. 3, No.2, 2011.
[18] H. K. Khalil, "Non Linear dynamical Systems". Prentice Hall, (2002, 3rd edi.), NJ 07458, USA.
[19] Hahn, W., Stability of Motion. Springer, 1967.
[20] G. Chen, Int. J. Bifurcation Chaos 9 (7), 1999, pp. 1465
[21] G. H. Tigan, Proceedings of the 3rd International Colloquium, Mathematics in Engineering and Numerical Analysis Physics, Romania, Bucharest, 2004, 265-272.