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We propose here a local exponential divergence plot which is capable ofproviding a new means ofcharacterizing chaotic time series. The suggested plot defines a time dependent exponent A and a "plus" exponent A÷ which servesas a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time and the largest Lyapunov exponent, garded as distances between orbits, then if the moare intimately related to the problem of how to distion is truly chaotic, points with dis(Xa+k, XJ+k)> tinguish chaos from stochastic processes. Therefore, dis(X1, X~)will dominate and lie above the zero level it would be very helpful if a geometric method could line in the plot. be devised to view the dynamics, especially the local Figure 1 shows divergence plots with different m exponential divergence dominated behaviorof a time and L for the Rössler attractor (a = 0.15, b = 0.20, series, so that a glance at this divergence plot would c= 10.0, &t= 7t/25, the dynamics is reconstructed provide some insight into the dynamic system.from the x component of the flow). We will show We report here a kind of local exponential diverbelow that the difference between these plots gives gence plot which enables one to view the dynamics a hint to optimal embedding, and m =3, L =8 coron a chaotic attractor. The simple plot provides a respond to optimal parameter values. The zero level criterion for the selection of the minimal acceptable line is added to fig. lb for a clear view of the diverembedding dimension and an optimal delay time.gence dominated behavior. When the unstable motion on the chaotic attractor A problem of significant practical importance is to only is extracted, a proper estimation of the largest determine the minimum acceptable embedding dipositive Lyapunov exponent can also be obtained. mension m~. A basic idea is that in the passage from Assume we have a time series x1, x2, ..., with samdimension m to m + 1 one can differentiate between 0375-9601/93/S 06.00

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