Collective patterns of swarm dynamics and the Lyapunov analysis of individual behaviors

Masashi Shiraishi, Yoji Aizawa

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


In this report, the collective patterns of swarms dynamics are theoretically studied using a self-propelled particle model, and the dynamics of the individual particles in the swarms is precisely studied using Lyapunov analysis. Furthermore, the collective behaviors of the swarms are classified into several patterns characterized by the following statistical quantities: Lyapunov spectrum, Lyapunov dimension, and stability and instability indices. Consequently, we propose individual instability exponents (IIEs) that describes the sensitivity of the individual particles in the swarm, and show that the IIEs is a significant order parameter that demonstrates changes in the pattern and expresses the activity of the swarm dynamics. Furthermore, we show that the mean and variance obtained after calculating the speed distribution of individual particles reveal marked variations corresponding to the change in the pattern in a manner similar to those of the IIEs.

Original languageEnglish
Article number054002
JournalJournal of the Physical Society of Japan
Issue number5
Publication statusPublished - 2015 May 15

ASJC Scopus subject areas

  • General Physics and Astronomy


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