A new approach to generalized chaos synchronization based on the stability of the error system. (English) Zbl 1172.93015

Summary: With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of Generalized Synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity. Further generalization and appropriation can be acquired without a stability requirement for the chaotic system’s linear part. The Lorenz system and a hyperchaotic system are taken for illustration and verification and the results of the simulation indicate that the method is effective.


93B55 Pole and zero placement problems
93C10 Nonlinear systems in control theory
37N35 Dynamical systems in control
58E25 Applications of variational problems to control theory
Full Text: EuDML Link


[1] Carroll L., Pecora M.: Synchronizing chaotic circuits. IEEE Trans. Circuits and Systems 38 (2001), 4, 453-456 · Zbl 1058.37538
[2] Chua L. O.: Experimental chaos synchronization in Chua’s circuit. Internat. J. Bifurc. Chaos 2 (2002), 3, 705-708 · Zbl 0875.94133
[3] Dachselt F., Schwarz W.: Chaos and cryptography. IEEE Trans. Circuits and Systems, Fundamental Theory and Applications 48 (2001), 12, 1498-1509 · Zbl 0999.94030
[4] Elabbasy E. M., Agiza H. N., El-Dessoky M. M.: Controlling and synchronization of Rossler system with uncertain parameters. Internat. J. Nonlinear Sciences and Numerical Simulation 5 (2005), 2, 171-181 · Zbl 1086.37512
[5] Fang J. Q.: Control and synchronization of chaos in nonlinear systems and prospects for application 2. Progr. Physics 16 (1996), 2, 174-176
[6] Fang J. Q.: Mastering Chaos and Development High-tech. Atomic Energy Press, Beijing, 2002
[7] Gao Y., Weng J. Q., al. X. S. Luo et: Generalized synchronization of hyperchaotic circuit. J. Electronics 6 (2002), 24. 855-959
[8] Kapitaniak T.: Experimental synchronization of chaos using continuous control. Internat. J. Bifurc. Chaos 4 (2004), 2, 483-488 · Zbl 0825.93298
[9] Kocarev L., Parlitz U.: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys. Rev. Lett. 11 (1996), 76, 1816-1819
[10] Lorenz E. N.: Deterministic nonperiodic flow. J. Atmospheric Sci. 20 (1963), 1. 130-141 · Zbl 1417.37129
[11] Pecora M., Carroll L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 8, 821-823 · Zbl 0938.37019
[12] Pecora M., Carroll L.: Driving systems with chaotic signals. Phys. Rev. A 44 (2001), 4, 2374-2383
[13] Yang T., Chua L. O.: Generalized synchronization of chaos via linear transformations. Internat. J. Bifur. Chaos 9 (1999), 1, 215-219 · Zbl 0937.37019
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.