Complete synchronization of strictly different chaotic systems. (English) Zbl 1263.93087

Summary: The criteria for complete synchronization of strictly different chaotic systems using feedback control are presented in this paper. Complete synchronization is achieved when all the states in the slave system are synchronous with the corresponding state in the master system. We illustrate that using a single input and single output control scheme, the synchronization of a class of strictly different systems is obtained in partial form. To overcome this problem we show that a multiple input and multiple output control scheme with an equal number of inputs and outputs than the order system is required in order to obtain the complete synchronization. This procedure is used to synchronize the Rössler and the Chen systems as an example. We also demonstrate that if the synchronization scheme considers less inputs and outputs, the partial-state synchronization is obtained.


93B52 Feedback control
34D06 Synchronization of solutions to ordinary differential equations
93C35 Multivariable systems, multidimensional control systems
Full Text: DOI


[1] L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821-824, 1990. · Zbl 0938.37019
[2] R. Femat, R. Jauregui-Ortiz, and G. Solís-Perales, “A chaos-based communication scheme via robust asymptotic feedback,” IEEE Transactions on Circuits and Systems I, vol. 48, pp. 1161-1169, 2002.
[3] F. Pasemann, “Synchronized chaos and other coherent states for two coupled neurons,” Physica D, vol. 128, p. 1970, 1995. · Zbl 0942.92002
[4] A. Rodriguez-Angeles and H. Nijmeijer, “Mutual synchronization of robots via estimated state feedback: a cooperative approach,” IEEE Transactions on Control Systems Technology, vol. 12, no. 4, pp. 542-554, 2004.
[5] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, “Complex networks: structure and dynamics,” Physics Reports, vol. 424, no. 4-5, pp. 175-308, 2006. · Zbl 1371.82002
[6] X. F. Wang and G. Chen, “Synchronization in scale-free dynamical networks: robustness and fragility,” IEEE Transactions on Circuits and Systems, vol. 49, no. 1, pp. 54-62, 2002. · Zbl 1368.93576
[7] E. M. Elabbasy, H. N. Agiza, and M. M. El-Dessoky, “Adaptive synchronization of Lü system with uncertain parameters,” Chaos, Solitons and Fractals, vol. 21, no. 3, pp. 657-667, 2004. · Zbl 1062.34039
[8] Y. Yu and S. Zhang, “Adaptive backstepping synchronization of uncertain chaotic system,” Chaos, Solitons and Fractals, vol. 21, no. 3, pp. 643-649, 2004. · Zbl 1062.34053
[9] H. Fang, “Synchronization of two rank-one chaotic systems without and with delay via linear delayed feedback control,” Journal of Applied Mathematics, vol. 2012, Article ID 325131, 15 pages, 2012. · Zbl 1243.93035
[10] R. Femat and G. Solís-Perales, “On the chaos synchronization phenomena,” Physics Letters A, vol. 262, no. 1, pp. 50-60, 1999. · Zbl 0936.37010
[11] A. Isidori, Nonlinear Control Systems, Springer, Berlin, Germany, 2nd edition, 1989. · Zbl 0693.93046
[12] A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization a Universal Concept in Nonlinear Sciences, Cambridge Nonlinear Science Series 12, Cambridge University Press, Cambridge, UK, 2001. · Zbl 0993.37002
[13] G. Solís-Perales, V. Ayala, W. Kliemann, and R. Femat, “Complete synchronizability of chaotic systems: a geometric approach,” Chaos, vol. 13, no. 2, pp. 495-501, 2003. · Zbl 1080.37544
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.