## Collective motion and oscillator synchronization (2003)

Venue: | Proc. Block Island Workshop on Cooperative Control |

Citations: | 27 - 8 self |

### BibTeX

@INPROCEEDINGS{Sepulchre03collectivemotion,

author = {Rodolphe Sepulchre and Derek Paley and Naomi Leonard},

title = {Collective motion and oscillator synchronization},

booktitle = {Proc. Block Island Workshop on Cooperative Control},

year = {2003},

pages = {189--228}

}

### Years of Citing Articles

### OpenURL

### Abstract

Summary. This paper studies connections between phase models of coupled oscillators and kinematic models of groups of self-propelled particles. These connections are exploited in the analysis and design of feedback control laws for the individuals that stabilize collective motions for the group. 1

### Citations

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Citation Context ...nchronization 17 on the network connectivity but extending the analysis to these situations is not straightforward. Recent convergence results for the Viczek model under weak connectivity assumptions =-=[JLM02]-=- provide new analysis tools for such generalizations. The stabilization problems treated in this paper are considered a preliminary step to more challenging design problems such as path planning or co... |

403 |
Chemical Oscillations, Waves and Turbulence
- Kuramoto
- 1984
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Citation Context ... has been studied in e.g. Ermentrout and Kopell [EK90] and Hoppensteadt and Izhikevich [HI97]. Even with the simplest type of coupling (3), the phase model (4), then referred to as the Kuramoto model =-=[Kur84]-=-, exhibits rich dynamics and has received considerable attention in the literature. Analytical results have been obtained for the continuous limit of N → ∞ (see Strogatz [Str00] for a recentsCollectiv... |

320 | Novel type of phase transition in a system of self-driven particles - Vicsek, Czirók, et al. - 1995 |

164 | 2000] “From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators
- Strogatz
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Citation Context ... as the Kuramoto model [Kur84], exhibits rich dynamics and has received considerable attention in the literature. Analytical results have been obtained for the continuous limit of N → ∞ (see Strogatz =-=[Str00]-=- for a recentsCollective motion and oscillator synchronization 5 review). In the finite case, results are mostly restricted to the situation of identical natural frequencies: ωk = ω, 1 ≤ k ≤ N. (The c... |

125 |
Weakly connected neural networks
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- 1997
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Citation Context ...g, the reduction of higher-dimensional models to (4) by asymptotic methods (singular perturbations and averaging) has been studied in e.g. Ermentrout and Kopell [EK90] and Hoppensteadt and Izhikevich =-=[HI97]-=-. Even with the simplest type of coupling (3), the phase model (4), then referred to as the Kuramoto model [Kur84], exhibits rich dynamics and has received considerable attention in the literature. An... |

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Selforganization in systems of self-propelled particles
- Levine, Rappel, et al.
- 2000
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Citation Context ...ar orbits of the particles around a fixed point. Both types of motion have been observed in simulations in a number of models that are kinematic or dynamic variants of the model (1), see for instance =-=[LRC01]-=-. A simplification of the model (1) occurs when the feedback laws depend on relative orientations only (u spac k ≡ 0). The control has then a much larger symmetry group (N copies of the translation gr... |

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Citation Context ...j ) + 0(ɛ 2 ) . (25) The controls u spac k , 1 < k ≤ N can now be determined to assign formations for the group of particles moving in parallel. As an illustration, we follow the approach proposed in =-=[BL02]-=- to stabilize formations of (non-oriented) particles: the desired formation is specified by the critical points of a scalar potential N� � U = UI(rij) i=1 j>i where the potential UI(rij) = UI(ri − rj)... |

32 |
Oscillator death in systems of coupled neural oscillators
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- 1990
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Citation Context ...e. Under the assumption of weak coupling, the reduction of higher-dimensional models to (4) by asymptotic methods (singular perturbations and averaging) has been studied in e.g. Ermentrout and Kopell =-=[EK90]-=- and Hoppensteadt and Izhikevich [HI97]. Even with the simplest type of coupling (3), the phase model (4), then referred to as the Kuramoto model [Kur84], exhibits rich dynamics and has received consi... |

29 | A simple control law for UAV formation flying
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Citation Context ... as reconfigurable moving sensor arrays for data collection in the ocean [II03]. The particle model we consider in this paper is a (kinematic) model of self-propelled particles recently introduced in =-=[JK02]-=-. Each particle moves at constant speed in the plane but adapts its orientation (i.e. the direction of its unit velocity vector) according to the motion of neighboring particles. The state space of ea... |

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Constants of motion for superconducting josephson arrays. Phys. D
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- 1994
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Citation Context ... then become equivalent to phase models of N coupled oscillators in which each oscillator is only modelled by a phase variable. Remarkable analysis results have been obtained by Watanabe and Strogatz =-=[WS94]-=- for phase models of coupled oscillators under the particular assumption of (all-to-all) pure sinusoidal coupling. They showed that this model possesses N − 3 constants of motion and provided a global... |