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Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals. (English) Zbl 1180.37040
Summary: The issue of impulsive synchronization of a hyperchaotic Lorenz system is developed. We propose an impulsive synchronization scheme of the hyperchaotic Lorenz system including chaotic systems. Some new and sufficient conditions on varying impulsive distances are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived for synchronizing the systems by equal impulsive distances. The boundaries of the stable regions are also estimated. Simulation results show the proposed synchronization method to be effective.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Thamilmaran, K.; Lakshmanan, M.; Venkatesan, A., Hyperchaos in a modified canonical chua’s circuit, Internat. J. bifur. chaos, 14, 221-243, (2004) · Zbl 1067.94597
[2] G. Grassi, S. Mascolo, Design of nonlinear observer for hyperchaos synchronization using s scalar signal, in: Proc IEEE Int. Symp on Circuits and Systems 3, 1998, pp. 283-289
[3] Li, Y.X.; Tang, S.; Chen, G.R., Generating hyperchaos via state feedback control, Int. J. circuit theory appl., 15, 3367-3375, (2005)
[4] Chen, A.M.J.; Lu, A.; Lü, J.H.; Yu, S.M., Generating hyperchaotic Lu attractor via state feedback control, Physica A, 364, 103-110, (2006)
[5] Yan, Z.Y., Controlling hyperchaos in the new hyperchaotic Chen system, Appl. math. comput., 168, 1239-1250, (2005) · Zbl 1160.93384
[6] Wang, F.Q.; Liu, C.X., Synchronization of hyperchaotic Lorenz system based on passive control, Chin. phys., 15, 1971-1976, (2006)
[7] Peng, J.H.; Ding, E.J.; Ding, M.; Yang, W., Synchronizing hyperchaos with a scalar transmitted signal, Phys. rev. lett., 76, 904-907, (1996)
[8] D. Cafagna, G. Grassi, Synchronizing hyperchaos using a scalar signal: A unified framework for systems with one or several nonlinearities, in: Asia-Pacific Conference on Circuit Systems APCCAS 02, 28, 2002, pp. 575-580
[9] Itoh, M.; Yang, T.; Chua, L.O., Conditions for impulsive synchronization of chaotic and hyperchaotic system, Internat. J. bifur. chaos appl., 11, 551-560, (2001) · Zbl 1090.37520
[10] Stojanovski, T.; Kocarev, L.; Parlitz, U.; Harris, R., Controlling spatiotemporal chaos in coupled nonlinear oscillators, Phys. rev. E, 56, 1238-1241, (1997)
[11] Li, C.D.; Liao, X.F., Complete and lag synchronization of hyperchaotic systems using small impulses, Chaos solitons fractals, 22, 857-867, (2004) · Zbl 1129.93508
[12] Yang, T.; Yang, L.B.; Yang, C.M.A., Ge semiconductor experiment showing chaos and hyperchaos, Physica D, 35, 425-435, (1997)
[13] Zhang, P.; Sun, J.T., Stability of impulsive delay differential equations with impulses at variable times, Internat. J. dynam. syst., 20, 323-331, (2005) · Zbl 1088.34069
[14] Sun, J.T.; Zhang, Y.P., Impulsive control and synchronization of chua’s oscillators, Math. comput. simul., 66, 499-508, (2004) · Zbl 1113.93088
[15] Li, C.; Feng, G.; Huang, T., On hybrid impulsive and switching neural networks, IEEE trans. syst. man cybern. part B, 28, 233-238, (2008)
[16] Huang, T.; Li, C.; Liu, X., Synchronization of chaotic systems with delay using intermittent linear state feedback, Chaos, 18, 331-342, (2008)
[17] Huang, T.; Li, C.; Liao, X., Synchronization of a class of coupled chaotic delayed systems with parameter mismatch, Chaos, 17, 321-331, (2007)
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