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Clusters of biological organisms often show diverse collective motions. Considering the physical properties of active elements with mutual interactions, we propose a mathematical model of collective motion. Several kinds of cluster motion seen in nature, including collective rotation, chaos, and wandering, occur in computer simulations of our deterministic model. By introducing a set of dimensionless parameters, we categorize the collective motions and obtain their phase diagram. We analyze the collective motions with a disorder parameter and Lyapunov spectra to characterize their transitions.
Shimoyama et al. (1996) studied this question.