Experimental robust synchronization of hyperchaotic circuits. (English) Zbl 1179.37047

A strategy for the design of an observer for hyperchaotic circuits is discussed. In particular, the proposed strategy is based on the Master Stability Function (MSF) approach. The robustness of synchronization in the presence of parametric uncertainties in the observed systems is investigated, both numerically and experimentally. The experiment is performed through the electrical analogue of a recently introduced Lorenz-like system able to show hyperchaotic behavior. Dealing with real circuit components, the two coupled circuits cannot be identical, due to the tolerances in electrical components. However, the study performed and the results obtained show that a suitable level of synchronization can also be reached in the presence of parameter mismatches. This allows to say that the MSF approach is a robust observer design tool for critical systems such as hyperchaotic ones.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI


[1] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 61, 821-824 (1990) · Zbl 0938.37019
[2] Buscarino, A.; Fortuna, L.; Frasca, M., Separation and synchronization of chaotic signals by optimization, Phys. Rev. E, 75, 016215 (2007)
[3] Arena, P.; Buscarino, A.; Fortuna, L.; Frasca, M., Separation and synchronization of piecewise linear chaotic systems, Phys. Rev. E, 74, 026212 (2006)
[4] Fortuna, L.; Frasca, M., Experimental synchronization of single-transistor-based chaotic circuits, Chaos, 17, 043118 (2007) · Zbl 1163.37325
[5] Matsumoto, T.; Chua, L. O.; Kobayashi, K., Hyperchaos: Laboratory experiment and numerical confirmation, IEEE Trans. Circuits Syst., 33, 1143-1147 (1986)
[6] Peng, J. H.; Ding, E. J.; Ding, M.; Yang, W., Synchronizing hyperchaos with a scalar transmitted signal, Phys. Rev. Lett., 76, 904-907 (1996)
[7] Tamaševičius, A.; Čenys, A., Synchronizing hyperchaos with a single variable, Phys. Rev. E, 55, 297-299 (1997)
[8] Grassi, G.; Mascolo, S., Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal, IEEE Trans. Circuits Syst.-I, 44, 1011-1914 (1997)
[9] Rössler, O. E., An equation for hyperchaos, Phys. Lett. A, 71, 155 (1979) · Zbl 0996.37502
[10] Pyragas, K., Predictable chaos in slightly perturbed unpredictable chaotic systems, Phys. Lett. A, 181, 203 (1993)
[11] Wang, J.; Chen, Z.; Chen, G.; Yuan, Z., A novel hyperchaotic system and its complex dynamics, Int. J. Bif. Chaos, 18, 3309 (2009) · Zbl 1165.34355
[12] Manganaro, G.; Arena, P.; Fortuna, L., Cellular Neural Networks: Chaos, Complexity and VLSI Processing (1999), Springer-Verlag: Springer-Verlag New York · Zbl 0976.68124
[13] Kapitaniak, T., Synchronization of chaos using continuous control, Phys. Rev. E, 50, 1642-1644 (1994)
[14] Amritkar, R. E.; Gupte, N., Synchronization of chaotic orbits: The effect of a finite time step, Phys. Rev. E, 47, 3889-3895 (1993)
[15] Kocarev, L.; Parlitz, U., General approach for chaotic synchronization with applications to communication, Phys. Rev. Lett., 74, 5028-5031 (1995)
[16] Parlitz, U.; Kocarev, L.; Stojanovski, T.; Preckel, H., Encoding messages using chaotic synchronization, Phys. Rev. E, 53, 4351-4361 (1996)
[17] Guemez, J.; Matias, M. A., Modified method for synchronizing and cascading chaotic systems, Phys. Rev. E, 52, R2145-R2148 (1995)
[18] Boccaletti, S.; Kurths, J.; Osipov, G.; Vallardes, D. L.; Zhou, C. S., The synchronization of chaotic systems, Phys. Rep., 366, 1-101 (2002) · Zbl 0995.37022
[19] Pecora, L. M.; Carroll, T. L., Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80, 2109-2112 (1998)
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.