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.<\/p>\r\n","references":"[1]\tE. Lorenz, \"Deterministic nonperiodic flow,\u201d Journal of the Atmospheric Sciences, \tvol. 20, no. 2, 1963, pp. 130\u2013141. \r\n[2]\tL. Pecora and T. Carroll, Synchronization in Chaotic Systems. Phys. Rev. Lett. 64, 1990, pp.821\u2013 823.\r\n[3]\tYan-Ni li, et al., .Experimental study of chaos synchronization in the Belousov\u2013\tZhabotinsky chemical \tsystem. Chaos, Solitons and Fractals, Vol. 22, issue.14, 2004, pp.767-771.\r\n[4]\tA. N. Pisarchik, et al., Synchronization of Shilnikov Chaos in a CO2 Laser with \tfeedback. Laser Physics, \tVol. 11, No. 11, 2001, pp. 1235\u20131239.\r\n[5]\tOlga Moskalenko, et al., Generalized synchronization of chaos for secure \tcommunication: remarkable stability to noise. Phys. Lett. A. 374, 2010, pp. 2925-2931.\r\n[6]\tY. Lei, et al., Synchronization of two chaotic nonlinear gyros using active control, \tPhy. Lett. A, 343, 2005, pp. 153-158\r\n[7]\tM. 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.\r\n[8]\tM. Shahzad, Israr Ahmad. Experimental Study of Synchronization & Anti-\tsynchronization for Spin Orbit Problem of Enceladus. International Journal of \tControl Science and Engineering, 3(2), 2013, pp. 41-47.\r\n[9]\tVaidyanathan. Adaptive Controller and Synchronization Design for Hyperchaotic \tZhou Systems with unknown Parameters. IJITMC Vol.1, No.1 (2013).\r\n[10]\tHsien- keng Chen. Global chaos synchronization of new chaotic systems via non-\tlinear control. Chaos, Solitons and Fractals 23, 2005, pp. 1245-1251.\r\n[11]\tDaolin XU and Zhigang LI. Controlled Projective Synchronization in Nonpartially-\tLinear Chaotic systems. International Journal of Bifurcation and Chaos, Vol. 12, \tNo. 6, 2002, pp. 1395-1402.\r\n[12]\tE. Vincent. Chaos synchronization using Active control and Backsteeping Control. \tNonlinear Any: Modelling & Control, Vol. 13, No. 2, 2008, pp. 253-261.\r\n[13]\t\tG. P. Jiang, et al., A global synchronization criterion for coupled chaotic systems \tvia unidirectional linear \terror state feedback approach. Int. J. Bifurcation Chaos, \tVol. 12, No. 10, 2002, pp. 2239-2253.\r\n[14]\tMehmet Akbar, Umit Ozguner, Decenterilization Sliding Mode Control Design \tusing overlapping decomposition. \tAutometica 38, 2002, pp. 1713-1718.\r\n[15]\tV. Sundarapandian. Global Chaos Anti-Synchronization of Tigan and Lorenz by Nonlinear Control. International Journal of Mathematical Sciences and Applications, Vol. 1, No.2, 2011.\r\n[16]\tV. Sundarapandian. Hybrid Synchronization of Liu and Chen systems by Active Nonlinear control. International Journal of Mathematical Sciences and Applications, \tVol. 1, No.3, 2011. \r\n[17]\tV.Sundarapandian. Hybrid Synchronization of Liu-Chen and Tigan systems by Active Nonlinear Control. \tInternational Journal of Advances in Science and \tTechnology, Vol. 3, No.2, 2011.\r\n[18]\tH. K. Khalil, \"Non Linear dynamical Systems\". Prentice Hall, (2002, 3rd edi.), NJ \t07458, USA.\r\n[19]\tHahn, W., Stability of Motion. Springer, 1967.\r\n[20]\tG. Chen, Int. J. Bifurcation Chaos 9 (7), 1999, pp. 1465\r\n[21]\tG. H. Tigan, Proceedings of the 3rd International Colloquium, Mathematics in \tEngineering and Numerical Analysis Physics, Romania, Bucharest, 2004, 265-272.\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 84, 2013"}