Lyapunov analysis of collective behaviors in self-propelled particle systems

Masashi Shiraishi, Yoji Aizawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We study the detailed mechanism of collective behaviors in self-propelled particle (SPP) systems by using Lyapunov exponents spectrum. We treat a simple 2-dimensional continuous time dynamical model, which includes the self-controlling effect as well as the interaction effect in the swarm. It is shown that the swarm reveals three types of cohesive clustering modes corresponding to marching, rotating, and swarming. Those modes appear alternatively and intermittently in the course of time in general. We elucidate the stability/instability of these cohesive states from the Lyapunov exponents related to the stretching or contracting manifolds. Furthermore, it is shown that the clustering ratio approaches to unity when the number of particles goes to large enough, and that the size dependence of the clustering ratio is clearly shown by the Lyapunov dimension. These numerical results seem to suggest that the tangent space plays an essential role in self-organization of collective swarm dynamics.

Original languageEnglish
Title of host publicationProceedings of the SICE Annual Conference
PublisherSociety of Instrument and Control Engineers (SICE)
Pages866-871
Number of pages6
ISBN (Print)9784907764463
DOIs
Publication statusPublished - 2014 Oct 23
Event2014 53rd Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2014 - Sapporo
Duration: 2014 Sep 92014 Sep 12

Other

Other2014 53rd Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2014
CitySapporo
Period14/9/914/9/12

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Keywords

  • Collective Behavior
  • Lyapunov Analysis
  • Self-Propelled Particles
  • Swarm

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications

Cite this

Shiraishi, M., & Aizawa, Y. (2014). Lyapunov analysis of collective behaviors in self-propelled particle systems. In Proceedings of the SICE Annual Conference (pp. 866-871). [6935230] Society of Instrument and Control Engineers (SICE). https://doi.org/10.1109/SICE.2014.6935230