A New Classification of Strange Attractors of Chaos from Mutual Information
N. Okamura, Hisao Okamoto, Shoji Tomii · Institutional Repositories DataBase (IRDB) · 1997
Abst rac t. A new criterion to classify chaotic dynamics using mutual informa-tion is proposed. The mutual information (MI) is examined for four model dy-namical systems, i.e., HBnon map, standard map, driven damped pendulum and Duffing equation (Ueda's Japanese attractor). A similar algorithm for calculat-ing MI proposed by A.M.Fraser and H.L.Swinney (Phys.Rev.A33(1986)1134) is used and the temporal variation of MI is examined for a long time interval, e.g., more than 500 times of the average period T of each PoincarB cycle of the dynamical system. Two characteristic features in the teporal variation of MI are found out. In one of the two cases MI decays to zero rapidly in a few times of T less than 10T, in the other case MI also decays to some fineite value M I, within 10T in the earlier stage, and MI fluctuates around M I, which does not vanish even for greater than 500T in the present calculation. The numerical value of M I, persists around 13 % of an initial value of MI. In the present study, HBnon map, driven damped pendulum and Duffing equation belong to the lapidly decaying-out type of MI, but standard map belongs to the persis-tent type with finite MI,. Thus the dynamical feature of chaotic behavior could be classified into two types using a mutual information. 1.