{"title":"Synchronization of Non-Identical Chaotic Systems with Different Orders Based On Vector Norms Approach","authors":"Rihab Gam, Anis Sakly, Faouzi M'sahli","volume":71,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":1606,"pagesEnd":1612,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10364","abstract":"
A new strategy of control is formulated for chaos synchronization of non-identical chaotic systems with different orders using the Borne and Gentina practical criterion associated with the Benrejeb canonical arrow form matrix, to drift the stability property of dynamic complex systems. The designed controller ensures that the state variables of controlled chaotic slave systems globally synchronize with the state variables of the master systems, respectively. Numerical simulations are performed to illustrate the efficiency of the proposed method.<\/p>\r\n","references":"[1] Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys Rev\r\nLett 1990:821-4.\r\n[2] Bai EW, Lonngren KE. Sequential synchronization of two Lorenz systems using active control. Chaos, Solitons & Fractals 2000:1041-4.\r\n[3] S. Hammami, K. Ben Saad, M. Benrejeb. On the synchronization of\r\nidentical and non-identical 4-D chaotic systems using arrow form matrix.\r\nChaos, Solitons and Fractals 42 (2009) 101-112.\r\n[4] Shih-Yu Li, Zheng-Ming Ge. Generalized synchronization of chaotic\r\nsystems with different orders by fuzzy logic constant controller. Expert\r\nsystems with application 38 (2011) 2302-2310.\r\n[5] Gentina JC, Borne P. Sur une condition d-application du crit\u00e8re de stabilit\u00e9 lin\u00e9aires \u251c\u00e1 certaines classes de syst\u00e8mes continus non lin\u00e9aires.\r\nCRAS, Paris, T. 275; 1972, p. 401-404.\r\n[6] Benrejeb M, Gasmi M. On the use of an arrow form matrix for modelling and stability analysis of singularly perturbed non linear\r\nsystems. SAMS 2001 40:509-25.\r\n[7] S. Hammami, M. Benrejeb, M. Feki, P. Borne. Feedback control design\r\nfor R\u00f6ssler and Chen chaotic systems anti-synchronization. Physics Letters A 374 (2010) 2835-2840.\r\n[8] Chen HK. Synchronization of two different chaotic systems: a new\r\nsystem and each of the dynamical systems Lorenz, Chen and Liu. Chaos,\r\nSolitons & Fractals 2005:1049-56.\r\n[9] U.E. Vincent. Synchronization of identical and non-identical 4-D chaotic\r\nsystems using active control. Chaos, Solitons and Fractals 37 (2008)\r\n1065-1075.\r\n[10] Juhn-Horng Chen a, Hsien-Keng Chen b,*, Yu-Kai Lin a. Synchronization and anti-synchronization coexist in Chen-Lee chaotic\r\nsystems. Chaos, Solitons and Fractals 39 (2009) 707-716.\r\n[11] Y.J. Sun, Solution bounds of generalized Lorenz chaotic systems, Chaos,\r\nSolitons & Fractals (2007), doi:10.1016\/j.chaos.2007.08.015.\r\n[12] Nijmeijer H, Mareels IMY. An observer looks at synchronization. IEEE\r\nTrans Circ Syst I 1997:882-90.\r\n[13] Mbouna Ngueuteu GS, Yamapi R, Woafo P. Effects of higher\r\nnonlinearity on the dynamics and synchronization of two coupled\r\nelectromechanical devices. Commun Nonlinear Sci Numer Simul\r\n2006:1213-40.\r\n[14] Osipov G et al. Phase synchronization effects in a lattice of non-identical\r\nR\u00f6ssler attractors. Phys Rev E 1997:2353-61.\r\n[15] Ho MC, Hung YC. Synchronization of two different systems by using\r\ngeneralized active control. Phys Lett A 2002:424-8.\r\n[16] Benrejeb M, Borne P, Laurent F. Sur une application de la repr\u00e9sentation\r\nen fl\u00e8che \u251c\u00e1 l-analyse des processus. RAIRO Automatique\/Systems\r\nAnalysis and Control 1982;16(2):133-46.\r\n[17] Borne P, Benrejeb M. On the representation and the stability study of\r\nlarge scale systems. In: Proceedings of ICCCC conference, B\u251c\u00faile Felix\r\nSpa-Oradea, Romania; May 2008.\r\n[18] M. Chen, D. Zhou, Y. Shang, A new observer-based synchronization\r\nscheme for private communication, Chaos, Solitons & Fractals 24 (2005)\r\n1025-1030.\r\n[19] S.H. Chen, Q. Yang, C.P. Wang, Impulsive control and synchronization\r\nof unified chaotic system, Chaos, Solitons & Fractals 20 (2004) 751- 758.\r\n[20] D.V. Efimov, Dynamical adaptive synchronization, International Journal\r\nof Adaptive Control and Signal Processing 20 (2006) 491-507.\r\n[21] H.T. Yau, C.S. Shieh, Chaos synchronization using fuzzy logic \r\ncontroller, Nonlinear Analysis: Real World Applications (2007), \r\ndoi:10.1016\/j.nonrwa.2007.05.009. \r\n[22] Y.P. Tian, X. Yu, Stabilizing unstable periodic orbits of chaotic systems \r\nvia an optimal principle, Journal of the Franklin Institute 337 (2000) \r\n771\u2013779. \r\n[23] S.M. Guo, L.S. Shieh, G. Chen, C.F. Lin, Effective chaotic orbit tracker: \r\na prediction-based digital redesign approach, IEEE Transactions on \r\nCircuits and Systems I 47 (2000) 1557\u20131560. ","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 71, 2012"}