Minimal mechanisms for school formation in self-propelled particles

Li, Yuexian; Lukeman, Ryan; Edelstein‐Keshet, Leah

doi:10.1016/j.physd.2007.10.009

Cited by 53 publications

(49 citation statements)

References 21 publications

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“…The "attraction", "repulsion" and "velocity mimicking" are loosely stated here and can take a wide range of forms. This modeling based on social forces finds its roots in the works of [1,27] for fish schooling and it has been widely used, expanded, and improved by theoretical biologists, physicists and applied mathematicians; see [15,34,29,24,30,44,45,3,31,32,19] and the references therein. This approach has been made much more specific for particular animals and species as in [5,4,47,25] for fish (studying migration patterns for the capelin around Iceland) and in [2,26] for birds (starlings grouping in Rome).…”

Section: Individual-based Modelsmentioning

confidence: 99%

Collective Behavior of Animals: Swarming and Complex Patterns

Cañizo¹,

Carrillo²,

Rosado³

2010

Arbor

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RESUMEN: En esta nota repasamos algunos modelos basados en individuos para describir el movimiento colectivo de agentes, a lo ABSTRACT:In this short note we review some of the individual based models of the collective motion of agents, called swarming. These models based on ODEs (ordinary differential equations) exhibit a complex rich asymptotic behavior in terms of patterns, that we show numerically. Moreover, we comment on how these particle models are connected to partial differential equations to describe the evolution of densities of individuals in a continuum manner. The mathematical questions behind the stability issues of these PDE (partial differential equations) models are questions of actual interest in mathematical biology research.

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Section: Individual-based Modelsmentioning

confidence: 99%

Collective Behavior of Animals: Swarming and Complex Patterns

Cañizo¹,

Carrillo²,

Rosado³

2010

Arbor

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“…These results suggest that the mill solution is unstable if the slope of the interaction function at d is either too large or too small (i.e., too steep). Stable mills exist when g (d) < 0, evidently due to the circular geometry, as linear formations studied in Li et al (2008) required that g (d) > 0.…”

Section: Numerical Investigationmentioning

confidence: 99%

“…In a companion paper Li et al (2008), a model for school formation was introduced based on the Lagrangian viewpoint, that is, following individual particles, rather than densities of organisms. Equations of motion were formulated based on the Newtonian approach, i.e., describing changes in the velocities and positions of the particles under forces of propulsion and interaction.…”

Section: Introductionmentioning

confidence: 99%

“…This self-propelled particle model was used to study perfect schools, which are configurations of particles in which the spacing is constant and identical, and where individuals in the group move at constant speed. One such perfect school in two dimensions, the soldier formation, was studied in Li et al (2008) using linear stability analysis. Analytic stability bounds were found in terms of the slope of the interaction force as a function of interindividual distance.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with linear aggregates (Li et al, 2008), the dynamics of the milling formation are significantly more complicated. The dependence of stability on the slope of the interaction function evaluated at interindividual distance is given in terms of a complexcoefficient quartic polynomial.…”

Section: Introductionmentioning

confidence: 99%

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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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Swarm Intelligence

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Minimal mechanisms for school formation in self-propelled particles

Cited by 53 publications

References 21 publications

Collective Behavior of Animals: Swarming and Complex Patterns

Collective Behavior of Animals: Swarming and Complex Patterns

A Conceptual Model for Milling Formations in Biological Aggregates

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