Zhang, Huaguang; Huang, Wei; Wang, Zhiliang; Chai, Tianyou Adaptive synchronization between two different chaotic systems with unknown parameters. (English) Zbl 1195.93121 Phys. Lett., A 350, No. 5-6, 363-366 (2006). Summary: A unified mathematical expression describing a class of chaotic systems is presented, for which the problem of adaptive synchronization between two different chaotic systems with unknown parameters has been studied. Based on Lyapunov stability theory, an adaptive synchronization controller is designed and analytic expression of the controller and the adaptive laws of parameters are developed. The adaptive synchronizations between Lorenz and Chen systems, a modified Chua’s circuit and Rössler systems are taken as two illustrative examples to show the effectiveness of the proposed method. Cited in 56 Documents MSC: 93D15 Stabilization of systems by feedback 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:chaotic system; adaptive chaos synchronization; different structure; unknown parameter PDFBibTeX XMLCite \textit{H. Zhang} et al., Phys. Lett., A 350, No. 5--6, 363--366 (2006; Zbl 1195.93121) Full Text: DOI References: [1] Ott, E.; Grebogi, C.; Yorke, J. A., Phys. Rev. Lett., 64, 1196 (1990) [2] Pyragas, K., Phys. Lett. A, 170, 421 (1992) [3] Wang, X. F.; Chen, G., IEEE Trans. Circuits Systems-I: Fund. Appl., 47, 410 (2000) [4] Zhang, H. G.; Wang, Z. L.; Liu, D. R., Int. J. Bifur. Chaos, 14, 1 (2004) [5] Yang, X. S.; Duan, C. K.; Liao, X. X., Chaos Solitons Fractals, 10, 1457 (1999) [6] Lü, J. H.; Zhou, T. S.; Zhang, S. C., Chaos Solitons Fractals, 14, 529 (2002) [7] Yin, X. H.; Ren, Y.; Shan, X. M., Chaos Solitons Fractals, 14, 1077 (2002) [8] Liao, T. L.; Tsai, S. H., Chaos Solitons Fractals, 11, 1387 (2000) [9] Han, X.; Lu, J. A.; Wu, X., Chaos Solitons Fractals, 22, 221 (2004) [10] Chen, S. H.; Lu, J. H., Chaos Solitons Fractals, 14, 643 (2002) [11] Sun, J. T.; Zhang, Y. P.; Wu, Q. D., Phys. Lett. A, 298, 153 (2002) [12] Chen, S. H.; Yang, Q.; Wang, C. P., Chaos Solitons Fractals, 20, 751 (2004) [13] Wang, Y. W.; Guan, Z. H.; Xiao, J. W., Chaos, 14, 199 (2004) [14] Bai, E. W.; Lonngren, K. E., Chaos Solitons Fractals, 11, 1041 (2000) [15] Ho, M. C.; Hung, Y. C., Phys. Lett. A, 301, 424 (2002) [16] Yassen, M. T., Chaos Solitons Fractals, 23, 131 (2005) · Zbl 1091.93520 [17] Huang, A.; Pivka, L.; Wu, C. W., Int. J. Bifur. Chaos, 6, 2175 (1996) 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.