Modified projective synchronization of chaotic system. (English) Zbl 1134.37331

Summary: A modified projective synchronization is proposed to acquire a general kind of proportional relationships between the drive and response systems. From rigorously control theory, a sufficient condition is attained for the stability of the error dynamics, and is applied to guiding the design of the controllers. Finally, we take the Lorenz system as an example for illustration and verification.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93D15 Stabilization of systems by feedback
Full Text: DOI


[1] Fujisaka, H.; Yamada, T., Stability theory of synchronized motion in coupled-oscillator systems, Progr Theor Phys, 69, 32-47 (1983) · Zbl 1171.70306
[2] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys Rev Lett, 64, 821-824 (1990) · Zbl 0938.37019
[3] Itoh, M.; Yang, T.; Chua, L. O., Conditions for impulsive synchronization of chaotic and hyperchaotic systems, Int J Bifur Chaos, 11, 551-560 (2001) · Zbl 1090.37520
[4] Yassen, M. T., Chaos synchronization between two different chaotic systems using active control, Chaos, Solitons & Fractals, 23, 131-140 (2005) · Zbl 1091.93520
[5] Rulkov, N. F.; Sushchik, M. M.; Tsimring, L. S., Generalized synchronization of chaos in directionally coupled chaotic systems, Phys Rev E, 51, 980-994 (1995)
[6] Kocarev, L.; Parlitz, U., Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems, Phys Rev Lett, 76, 1816-1819 (1996)
[7] Wang, Y. W.; Guan, Z. H., Generalized synchronization of continuous chaotic system, Chaos, Solitons & Fractals, 27, 97-101 (2006) · Zbl 1083.37515
[8] Kittel, A.; Parisi, J.; Pyragas, K., Generalized synchronization of chaos in electronic circuit experiments, Physica D, 112, 459-471 (1998) · Zbl 0930.37014
[9] Yan, J.; Li, C., Generalized projective synchronization of a unified chaotic system, Chaos, Solitons & Fractals, 26, 1119-1124 (2005) · Zbl 1073.65147
[10] Wen, G.; Xu, D., Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems, Chaos, Solitons & Fractals, 26, 71-77 (2005) · Zbl 1122.93311
[11] Grassi, G.; Mascolo, S., Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal, IEEE Trans Circ Syst I, 44, 1011-1014 (1997)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.