Zhao, Jiakun; Wu, Ying; Wang, Yuying Adaptive function Q-S synchronization of different chaotic (hyper-chaotic) systems. (English) Zbl 1277.34069 Int. J. Mod. Phys. B 27, No. 20, Article ID 1350109, 9 p. (2013). Summary: This paper presents the general method for the adaptive function Q-S synchronization of different chaotic (hyper-chaotic) systems. Based upon the Lyapunov stability theory, the dynamical evolution can be achieved by the Q-S synchronization with a desired scaling function between the different chaotic (hyper-chaotic) systems. This approach is successfully applied to two examples: Chen hyper-chaotic system drives the Lorenz hyper-chaotic system; Lorenz system drives Lü hyper-chaotic system. Numerical simulations are used to validate and demonstrate the effectiveness of the proposed scheme. MSC: 34D06 Synchronization of solutions to ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations 93C40 Adaptive control/observation systems 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 34H10 Chaos control for problems involving ordinary differential equations Keywords:function Q-S synchronization; chaotic system; hyper-chaotic system; scaling function; Lyapunov function PDFBibTeX XMLCite \textit{J. Zhao} et al., Int. J. Mod. Phys. B 27, No. 20, Article ID 1350109, 9 p. (2013; Zbl 1277.34069) Full Text: DOI References: [1] Perora L. M., Phys. Rev. Lett. 64 pp 821– [2] DOI: 10.1103/PhysRevLett.67.1953 · doi:10.1103/PhysRevLett.67.1953 [3] DOI: 10.1103/PhysRevLett.81.4835 · doi:10.1103/PhysRevLett.81.4835 [4] DOI: 10.1103/PhysRevLett.80.496 · doi:10.1103/PhysRevLett.80.496 [5] DOI: 10.1103/PhysRevE.70.067202 · doi:10.1103/PhysRevE.70.067202 [6] Xu J. F., Phys. Lett. 21 pp 1445– [7] DOI: 10.1016/S0370-1573(02)00137-0 · Zbl 0995.37022 · doi:10.1016/S0370-1573(02)00137-0 [8] DOI: 10.1016/j.physleta.2004.11.042 · Zbl 1123.37312 · doi:10.1016/j.physleta.2004.11.042 [9] DOI: 10.1016/S0960-0779(00)00089-8 · Zbl 1015.37052 · doi:10.1016/S0960-0779(00)00089-8 [10] DOI: 10.1016/0375-9601(76)90101-8 · Zbl 1371.37062 · doi:10.1016/0375-9601(76)90101-8 [11] DOI: 10.1142/S021812740200631X · Zbl 1043.37026 · doi:10.1142/S021812740200631X [12] DOI: 10.1016/j.na.2007.06.038 · Zbl 1153.34338 · doi:10.1016/j.na.2007.06.038 [13] Ben-Israel A., Generalized Inverse: Theory and Applications (1974) [14] B. R. Fang, J. D. Zhou and Y. M. Li, Matrix Theory (Tsinghua University Press, Beijing, 2004) pp. 256–262. [15] DOI: 10.1016/S0375-9601(99)00532-0 · Zbl 0939.34041 · doi:10.1016/S0375-9601(99)00532-0 [16] DOI: 10.1016/j.physleta.2006.09.042 · Zbl 1170.37308 · doi:10.1016/j.physleta.2006.09.042 [17] DOI: 10.1016/j.physa.2005.09.039 · doi:10.1016/j.physa.2005.09.039 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.