Pecora, Louis; Carroll, Thomas L. Synchronization in chaotic systems. (English) Zbl 0938.37019 Phys. Rev. Lett. 64, No. 8, 821-824 (1990). The paper opens a new direction of research, which promises to be very exciting. The authors derive an exceptional result concerning certain phenomena, that appeared intractable. Thus, although chaotic systems would seem to defy synchronization, certain subsystems can be made to synchronize by linking them with common signals. The condition is that the signs of the Lyapunov exponents for the subsystems are all negative. By synchronization it is understood that the trajectories of one of the systems converge to the same values as those of the other and that they then remain in step with each other. As the authors show, the synchronization appears to be structurally stable. The authors have investigated these phenomena on several models and in this paper they give the results for the Roessler and Lorenz attractors. They also briefly mention the construction of a real set of chaotic synchronizing circuits and some experimental results. Reviewer: Emanuel Cristian Savin (MR 92c:58082) Cited in 3 ReviewsCited in 2793 Documents MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37N35 Dynamical systems in control 94C05 Analytic circuit theory Keywords:synchronization; Lyapunov exponents; chaotic synchronizing circuits × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Y. S. Tang, IEEE Trans. Circuits 30 pp 620– (1983) · doi:10.1109/TCS.1983.1085409 [2] O. E. Rössler, Phys. Lett. 57A pp 397– (1976) · Zbl 1371.37062 · doi:10.1016/0375-9601(76)90101-8 [3] T. Matsumotot, IEEE Trans. Circuits Syst. 32 pp 798– (1985) [4] R. W. Newcomb, IEEE Trans. Circuits Syst. 30 pp 54– (1983) · doi:10.1109/TCS.1983.1085277 [5] T. L. Carroll, Phys. Rev. A 40 pp 377– (1989) · doi:10.1103/PhysRevA.40.377 [6] F. Mitschke, Appl. Phys. B 35 pp 59– (1984) · doi:10.1007/BF00697423 [7] , Rev. Mod. Phys. 57 pp 617– (1985) · Zbl 0989.37516 · doi:10.1103/RevModPhys.57.617 [8] O. E. Rössler, Z. Naturforsch. 38a pp 788– (1983) [9] C. Skarda, Behav. Brain Sci. 10 pp 161– (1987) [10] A. Garfinkel, Am. J. Physiol. 245 pp R455– (1983) [11] , in: Proceedings of the IEEE First Annual International Conference on Neural Networks, San Diego, 1987 (1987) [12] C. Skarda, Behav. Brain Sci. 10 pp 170– (1987) 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.