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 language | English |
|---|---|
| Title of host publication | Proceedings of the SICE Annual Conference |
| Publisher | Society of Instrument and Control Engineers (SICE) |
| Pages | 866-871 |
| Number of pages | 6 |
| ISBN (Print) | 9784907764463 |
| DOIs | |
| Publication status | Published - 2014 Oct 23 |
| Event | 2014 53rd Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2014 - Sapporo Duration: 2014 Sep 9 → 2014 Sep 12 |
Other
| Other | 2014 53rd Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2014 |
|---|---|
| City | Sapporo |
| Period | 14/9/9 → 14/9/12 |
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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
Lyapunov analysis of collective behaviors in self-propelled particle systems. / Shiraishi, Masashi; Aizawa, Yoji.
Proceedings of the SICE Annual Conference. Society of Instrument and Control Engineers (SICE), 2014. p. 866-871 6935230.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Lyapunov analysis of collective behaviors in self-propelled particle systems
AU - Shiraishi, Masashi
AU - Aizawa, Yoji
PY - 2014/10/23
Y1 - 2014/10/23
N2 - 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.
AB - 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.
KW - Collective Behavior
KW - Lyapunov Analysis
KW - Self-Propelled Particles
KW - Swarm
UR - http://www.scopus.com/inward/record.url?scp=84911897794&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84911897794&partnerID=8YFLogxK
U2 - 10.1109/SICE.2014.6935230
DO - 10.1109/SICE.2014.6935230
M3 - Conference contribution
AN - SCOPUS:84911897794
SN - 9784907764463
SP - 866
EP - 871
BT - Proceedings of the SICE Annual Conference
PB - Society of Instrument and Control Engineers (SICE)
ER -