Zhang, Wei; Huang, Junjian; Wei, Pengcheng Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control. (English) Zbl 1205.93125 Appl. Math. Modelling 35, No. 2, 612-620 (2011). Summary: This paper deals with the synchronization of two coupled identical chaotic systems with parameter mismatch via using periodically intermittent control. In general, parameter mismatches are considered to have a detrimental effect on the synchronization quality between coupled identical systems: in the case of small parameter mismatches the synchronization error does not decay to zero or even a nonzero mean. Larger values of parameter mismatches can even result in the loss of synchronization. via intermittent control with periodically intervals, we can obtain the weak synchronization. Some sufficient conditions for the stabilization and weak synchronization of a large class of coupled identical chaotic systems will be derived by using Lyapunov stability theory. The analytical results are confirmed by numerical simulations. Cited in 29 Documents MSC: 93D15 Stabilization of systems by feedback 37N35 Dynamical systems in control 34D06 Synchronization of solutions to ordinary differential equations 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:chaotic system; synchronization; intermittent control; parameter mismatch PDFBibTeX XMLCite \textit{W. Zhang} et al., Appl. Math. Modelling 35, No. 2, 612--620 (2011; Zbl 1205.93125) Full Text: DOI References: [1] Ott, E.; Grebogi, C.; Yorke, J. A., Controlling chaos, Rev. Lett., 64, 1196-1199 (1990) · Zbl 0964.37501 [2] Parlitz, U., Transmission of digital signals by chaotic synchronization, Int. J. Bifur. Chaos Appl. Sci. Eng., 2, 973-977 (1992) · Zbl 0870.94011 [3] Itoh, M.; Wu, C. W.; Chua, L. O., Communication systems via chaotic signals from a reconstruction viewpoint, Int. J. Bifur. Chaos Appl. Sci. Eng., 7, 275-286 (1997) · Zbl 0890.94007 [4] Bazhenov, M.; Huerta, R.; Rabinovich, M. I.; Sejnowski, T., Cooperative behavior of a chain of synaptically coupled chaotic neurons, Phys. D, 116, 392-400 (1998) · Zbl 0917.92004 [5] Collins, J. J.; Stewart, I. N., Coupled nonlinear oscillators and the symmetries of animal gaits, J. Nonlinear Sci., 3, 349-392 (1993) · Zbl 0808.92012 [6] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J., Phase synchronization of chaotic oscillators, Phys. Rev. Lett., 76, 1804-1807 (1996) [7] Rulkov, N. F.; Sushchik, M. M.; Tsimring, L. S.; Abarbanel, H. D.I., Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E, 51, 980-994 (1995) [8] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J., From phase to lag synchronization in coupled chaotic oscillators, Phys. Rev. Lett., 78, 4193-4196 (1997) [9] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019 [10] Pecora, M.; Carroll, T. L., Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80, 2109-2112 (1998) [11] Suykens, J. A.K.; Curran, P. F.; Vandewalle, J.; Chua, L. O., Robust nonlinear \(H\)-infinite synchronization Lur’e systems, IEEE Trans. Circuits Syst. I: Fundam. Theory Appl., 44, 891-904 (1997) [12] Zhang, Yu; Tao, Chao; Du, Gonghuan; Jiang, Jack J., Parameter estimations of parametrically excited pendulums based on chaos feedback synchronization, J. Sound Vib., 290, 3-5, 1091-1099 (2006) · Zbl 1243.93100 [13] Li, C. D.; Liao, X. F.; Huang, T. W., Chaos quasisynchronization induced by impulses with parameter mismatches, Chaos, 16, 023102 (2006) · Zbl 1146.37326 [14] Pyragas, K., Predictable chaos in slightly perturbed unpredictable chaotic systems, Phys. Lett. A, 181, 203-210 (1993) [15] Huang, T. W.; Li, C. D.; Liao, X. F., Synchronization of a class of coupled chaotic delayed systems with parameter mismatch, Chaos, 17, 033121 (2007) · Zbl 1163.37335 [16] Montgomery, T. L.; Frey, J. W.; Norris, W. B., Intermittent control systems, Environ. Sci. Technol., 9, 6, 528-532 (1975) [17] Zochowski, Michal, Intermittent dynamical control, Phys. D, 145, 181-190 (2000) · Zbl 0963.34030 [18] Li, C. D.; Liao, X. F.; Huang, T. W., Exponential stabilization of chaotic systems with delay by periodically intermittent control, Chaos, 17, 013103 (2007) · Zbl 1159.93353 [19] Boyd, S.; Ghaoui, L.; EI Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadephia [20] Shil’nikov, L. P., Chua’s circuit: rigorous results and future problems, Int. J. Bifur. Chaos Appl. Sci. Eng., 4, 489-519 (1999) · Zbl 0870.58072 This reference list is based on information provided by the publisher or from digital mathematics libraries. 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