Stability properties of the collective stationary motion of self-propelling particles with conservative kinematic constraints

Ratushnaya, V. I.; Bedeaux, Dick; Kulinskii, V. L.; Zvelindovsky, Andrei

doi:10.1088/1751-8113/40/10/021

Cited by 1 publication

(1 citation statement)

References 19 publications

(33 reference statements)

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“…Passing to the continuum limit often facilitates analysis by a reduction in order of the system, but this occurs at the cost of individual properties in favor of mean field properties. In Ratushnaya et al (2007), a linear stability analysis was performed on a vortex-type solution of a continuum model, but was inconclusive.…”

Section: Discussionmentioning

confidence: 99%

A Conceptual Model for Milling Formations in Biological Aggregates

Lukeman

Edelstein‐Keshet

2008

Bull. Math. Biol.

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Collective behavior of swarms and flocks has been studied from several perspectives, including continuous (Eulerian) and individual-based (Lagrangian) models. Here, we use the latter approach to examine a minimal model for the formation and maintenance of group structure, with specific emphasis on a simple milling pattern in which particles follow one another around a closed circular path.We explore how rules and interactions at the level of the individuals lead to this pattern at the level of the group. In contrast to many studies based on simulation results, our model is sufficiently simple that we can obtain analytical predictions. We consider a Newtonian framework with distance-dependent pairwise interaction-force. Unlike some other studies, our mill formations do not depend on domain boundaries, nor on centrally attracting force-fields or rotor chemotaxis.By focusing on a simple geometry and simple distant-dependent interactions, we characterize mill formations and derive existence conditions in terms of model parameters. An eigenvalue equation specifies stability regions based on properties of the interaction function. We explore this equation numerically, and validate the stability conclusions via simulation, showing distinct behavior inside, outside, and on the boundary of stability regions. Moving mill formations are then investigated, showing the effect of individual autonomous self-propulsion on group-level motion. The simplified framework allows us to clearly relate individual properties (via model parameters) to group-level structure. These relationships provide insight into the more complicated milling formations observed in nature, and suggest design properties of artificial schools where such rotational motion is desired.

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Section: Discussionmentioning

confidence: 99%