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**Synchronization in chaotic systems.**
*(English)*
Zbl 0938.37019

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)

### MSC:

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

37N35 | Dynamical systems in control |

94C05 | Analytic circuit theory |

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\textit{L. Pecora} and \textit{T. L. Carroll}, Phys. Rev. Lett. 64, No. 8, 821--824 (1990; Zbl 0938.37019)

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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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.