Wang, Zuo-Lei Projective synchronization of hyperchaotic Lü system and Liu system. (English) Zbl 1183.70055 Nonlinear Dyn. 59, No. 3, 455-462 (2010). Summary: This work is concerned with projective synchronization of hyperchaotic Lü system and Liu system by add-order method. Different controllers are designed to projective-synchronize the two nonidentical chaotic systems, active control is used when parameters are known, while the adaptive control law and the parameter update rule are derived via adaptive control when parameters are uncertain. Moreover, the convergence rates of the scheme can be adjusted by changing the control coefficients. Finally, numerical simulations are also shown to verify the results. Cited in 17 Documents MSC: 70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics Keywords:projective synchronization; chaos; hyperchaotic Lü system; Liu system PDFBibTeX XMLCite \textit{Z.-L. Wang}, Nonlinear Dyn. 59, No. 3, 455--462 (2010; Zbl 1183.70055) Full Text: DOI References: [1] Perora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990) · Zbl 0938.37019 [2] Boccaletti, S., Kurths, J., Osipov, G., Valladares, D.L., Zhou, C.S.: The synchronization of chaotic systems. Phys. Rep. 366, 1–101 (2002) · Zbl 0995.37022 [3] Luo, A.C.J.: A theory for synchronization of dynamical systems. Commun. Nonlinear Sci. Numer. Simul. 14, 1901–1951 (2009) · Zbl 1221.37218 [4] Yang, S.S., Juan, C.K.: Generalized synchronization in chaotic systems. Chaos Solitons Fractals 9, 1703–1707 (1998) · Zbl 0946.34040 [5] Yan, Z.Y.: Q–S synchronization in 3D Hénon-like map and generalized Hénon map via a scalar controller. Phys. Lett. A 342, 309–317 (2005) · Zbl 1222.37093 [6] Park, E.H., Zaks, M.A., Kurths, J.: Phase synchronization in the forced Lorenz system. Phys. Rev. E 60, 6627–6638 (1999) · Zbl 1062.37502 [7] Al-Sawalha, M.M., M-Noorani, M.S.: Chaos anti-synchronization between two novel different hyperchaotic systems. Chin. Phys. Lett. 25(8), 2743–2746 (2008) · Zbl 1188.70060 [8] Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82, 3042–3045 (1999) [9] Xu, D.: Control of projective synchronization in chaotic systems. Phys. Rev. E 63(2), 027201 (2001) [10] Chee, C.Y., Xu, D.: Secure digital communication using controlled projective synchronisation of chaos. Chaos Solitons Fractals 23(3), 1063–1070 (2005) · Zbl 1068.94010 [11] Xu, D., Chee, C.Y.: Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension. Phys. Rev. E 66(4), 046218 (2002) [12] Wen, G.L., Xu, D.: Observer-based control for full-state projective synchronization of a general class of chaotic maps in any dimension. Phys. Lett. A 333, 420–425 (2004) · Zbl 1123.37326 [13] Chee, C.Y., Xu, D.: Secure digital communication using controlled projective synchronization of chaos. Chaos Solitons Fractals 23(3), 1063–1070 (2005) · Zbl 1068.94010 [14] Xu, D., Li, Z.: Controlled projective synchronization in nonparametrically-linear chaotic systems. Int. J. Bifurc. Chaos 12(6), 1395–1402 (2002) [15] Li, Z., Xu, D.: A secure communication scheme using projective chaos synchronization. Chaos Solitons Fractals 22(2), 477–481 (2004) · Zbl 1060.93530 [16] Feng, C.F., Zhang, Y., Sun, J.T., Qi, W., Wang, Y.H.: Generalized projective synchronization in time-delayed chaotic systems. Chaos Solitons Fractals 38, 743–747 (2008) · Zbl 1146.37318 [17] Chen, A.M., Lu, J.A., Lü, J.H., Yu, S.M.: Generating hyperchaotic Lü attractor via state feedback control. Physica A 364, 103–110 (2006) [18] Liu, C., Liu, T., Liu, L., Liu, K.: A new chaotic attractor. Chaos Solitons Fractals 22, 1031–1038 (2004) · Zbl 1060.37027 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.