DIRECT DYNAMICAL TEST FOR DETERMINISTIC CHAOS AND OPTIMAL EMBEDDING OF A CHAOTIC TIME-SERIES

We propose here a local exponential divergence plot which is capable o f providing an alternative means of characterizing a complex time seri es. The suggested plot defines a time-dependent exponent and a ''plus' ' exponent. Based on their changes with the embedding dimension and de lay time, a criterion for estimating simultaneously the minimal accept able embedding dimension, the proper delay time, and the largest Lyapu nov exponent has been obtained. When redefining the time-dependent exp onent LAMBDA(k) curves on a series of shells, we have found that wheth er a linear envelope to the LAMBDA(k) curves exists can serve as a dir ect dynamical method of distinguishing chaos from noise.