Galias, Zbigniew Local transversal Lyapunov exponents for analysis of synchronization of chaotic systems. (English) Zbl 0983.37039 Int. J. Circuit Theory Appl. 27, No. 6, 589-604 (1999). The problem of synchronization of coupled chaotic systems is considered. Synchronization is studied by means of local transversal Lyapunov exponents. Using example of coupled Hénon maps and coupled hyperchaotic electronic systems, the developed criterion for synchronization is compared with other methods for an investigation of synchronization properties of unidirectionally coupled chaotic systems. Reviewer: Piotr Garbaczewski (Zielona Gora) Cited in 4 Documents MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 37M10 Time series analysis of dynamical systems 34D08 Characteristic and Lyapunov exponents of ordinary differential equations Keywords:chaotic signal; synchronization of coupled chaotic systems; Lyapunov exponents PDFBibTeX XMLCite \textit{Z. Galias}, Int. J. Circuit Theory Appl. 27, No. 6, 589--604 (1999; Zbl 0983.37039) Full Text: DOI References: [1] Fujisaka, Prog. Theor Phys. 69 pp 32– (1983) · Zbl 1171.70306 · doi:10.1143/PTP.69.32 [2] Afraimovich, Izv. VUZ Radiofiz. 29 pp 795– (1986) [3] Pecora, Phys. Rev. A. 44 pp 2374– (1991) · doi:10.1103/PhysRevA.44.2374 [4] Heagy, Phys. Rev. E 52 pp r1253– (1995) · doi:10.1103/PhysRevE.52.R1253 [5] , , ’Riddled basins and other practical problems in coupled synchronized chaotic circuits’, Chaotic Circuits for Communication, Proc. SPIE 2612, Phildelphia, 1995, pp. 25-36. [6] ’Transversal Lyapunov exponents and synchronization of chaotic systems’, Proc. European Conf. on Circuit Theory and Design, ECCTD’97, Budapest, 1997, pp. 1211-1215. [7] Galias, Int. J. Bifurcation Chaos 5 pp 281– (1995) · Zbl 0885.58047 · doi:10.1142/S0218127495000247 [8] Eckmann, Rev. Mod. Phys. 57 pp 617– (1985) · Zbl 0989.37516 · doi:10.1103/RevModPhys.57.617 [9] Grassberger, J. Statist. Phys. 51 pp 135– (1988) · Zbl 1086.37509 · doi:10.1007/BF01015324 [10] Analysis of Observed Chaotic Data, Springer, New York, 1996. · Zbl 0890.93006 · doi:10.1007/978-1-4612-0763-4 [11] ’Inclusion methods for systems of nonlinear equations–the interval newton method and modifications’, in (Ed.), Topics in Validated Computations, IMACS-GAMM, New Bounswick, NJ, 1994, pp. 7-26. · Zbl 0822.65029 [12] ’Existence and uniqueness of low-period cycles and estimation of topological entropy for the Hénon map’, Proc. Int. Symp. on Nonlinear Theory and its Applications, NOLTA’98, Vol. 1, Crans-Montana, 1998, pp. 187-190. [13] Matsumoto, IEEE Trans. Circuits Systems CAS-38 pp 1143– (1986) · doi:10.1109/TCS.1986.1085862 [14] ’Study of synchronization of linearly coupled hyperchaotic systems’, Proc. European Conf. on Circuit Theory and Design, ECCTD’97, Vol. 1, Budapest, 1997, pp. 296-301. [15] Lathrop, Phys. Rev. A 40 pp 4028– (1989) · doi:10.1103/PhysRevA.40.4028 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.