An algorithm to characterize collective motion as the orbital instability at a macroscopic level is presented, including the introduction of ``collective Lyapunov exponent.'' By applying the algorithm to a globally coupled map, existence of low-dimensional collective chaos is confirmed, where the scale of (high-dimensional) microscopic chaos is separated from the macroscopic motion, and the scale approaches zero in the thermodynamic limit.
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Shibata et al. (1998) studied this question.
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