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Attraction Based Models of Collective Motion
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Animal groups often exhibit highly coordinated collective motion in a variety of situations. For example, bird flocks, schools of fish, a flock of sheep being herded by a dog and highly efficient traffic on an ant trail. Although these phenomena can be observed every day all over the world our knowledge of what rules the individual's in such groups use is very limited. Questions of this type has been studied using so called self-propelled particle (SPP) models, most of which assume that collective motion arises from individuals aligning with their neighbors. Here we introduce and analyze a SPP-model based on attraction alone. We find that it produces all the typical groups seen in alignment-based models and some novel ones. In particular, a group that exhibits collective motion coupled with non-trivial internal dynamics. Groups that have this property are rarely seen in SPP-models and we show that even when a repulsion term is added to the attraction only model such groups are still present. These findings suggest that an interplay between attraction and repulsion may be the main driving force in real flocks and that the alignment rule may be superfluous.

We then proceed to model two different experiments using the SPP-model approach. The first is a shepherding algorithm constructed primarily to model experiments where a sheepdog is herding a flock of sheep. We find that in addition to modeling the specific experimental situation well the algorithm has some properties which may make it useful in more general shepherding situations. The second is a traffic model for leaf-cutting ants bridges. Based on earlier experiments a set of traffic rules for ants on a very narrow bridge had been suggested. We show that these are sufficient to produce the observed traffic dynamics on the narrow bridge. And that when extended to a wider bridge by replacing 'Stop' with 'Turn' the new rules are sufficient to produce several key characteristics of the dynamics on the wide bridge, in particular three-lane formation.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2013. , 35 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 82
Keyword [en]
flocking, swarming, self-propelled particles, alignment-free models, agent-based modelling, leaf-cutting ant traffic, sheep-sheepdog system, the Shepherding problem
National Category
Other Mathematics Ecology
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-205875ISBN: 978-91-506-2368-0 (print)OAI: oai:DiVA.org:uu-205875DiVA: diva2:645463
Public defence
2013-11-14, Polhemsalen, Lägerhyddsvägen 1, Uppsala, 15:15 (English)
Opponent
Supervisors
Available from: 2013-10-03 Created: 2013-08-23 Last updated: 2013-10-03
List of papers
1. Collective motion from local attraction
Open this publication in new window or tab >>Collective motion from local attraction
2011 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 283, no 1, 145-151 p.Article in journal (Refereed) Published
Abstract [en]

Many animal groups, for example schools of fish or flocks of birds, exhibit complex dynamic patterns while moving cohesively in the same direction. These flocking patterns have been studied using self-propelled particle models, most of which assume that collective motion arises from individuals aligning with their neighbours. Here, we propose a self-propelled particle model in which the only social force between individuals is attraction. We show that this model generates three different phases: swarms, undirected mills and moving aligned groups. By studying our model in the zero noise limit, we show how these phases depend on the relative strength of attraction and individual inertia. Moreover, by restricting the field of vision of the individuals and increasing the degree of noise in the system, we find that the groups generate both directed mills and three dynamically moving, 'rotating chain' structures. A rich diversity of patterns is generated by social attraction alone, which may provide insight into the dynamics of natural flocks.

Keyword
Self-propelled particle model, Collective motion, Flocking, Schooling, Local attraction
National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-167670 (URN)10.1016/j.jtbi.2011.05.019 (DOI)000298526600016 ()
Available from: 2012-02-01 Created: 2012-01-31 Last updated: 2017-12-08Bibliographically approved
2. The shape and dynamics of local attraction
Open this publication in new window or tab >>The shape and dynamics of local attraction
2015 (English)In: The European Physical Journal Special Topics, ISSN 1951-6355, E-ISSN 1951-6401, Vol. 224, no 17-18, 3311-3323 p.Article in journal (Refereed) Published
Abstract [en]

Moving animal groups, such as flocks of birds or schools of fish, exhibit complex internal dynamics while moving cohesively in the same direction. This kind of flocking behavior has been studied using self-propelled particle models, in which the `particles' interact with their nearest neighbors through repulsion, attraction and alignment responses. Recently, it has been shown that models based on attraction alone can generate a range of dynamic patterns. Here we investigate the conditions under which attraction-based models are able to reproduce the three dimensional, complex, dynamical patterns seen in natural animal groups. We provide a phase diagram of how attraction strength and blind angle determine the pattern generated in this model. We show that adding repulsion to the model changes the shapes produced, making them look more like natural flocking patterns. We compare our simulations to observations of surf scoters, starlings, moving and rotating fish schools and other flocks. Our results suggest that many biological instances of collective motion might be explained without animals explicitly responding to each others direction. Instead, complex collective motion is explained by the interplay of attraction and repulsion forces.

Keyword
collective motion, flocking, swarming, self-propelled particles
National Category
Ecology Other Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
urn:nbn:se:uu:diva-205880 (URN)10.1140/epjst/e2015-50082-8 (DOI)000367309500014 ()
Funder
EU, European Research Council
Available from: 2013-09-03 Created: 2013-08-23 Last updated: 2017-12-06Bibliographically approved
3. On stability and mobility of shapes in the local attraction model
Open this publication in new window or tab >>On stability and mobility of shapes in the local attraction model
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Many animal groups, for example schools of fish or flocks of birds, exhibit complex dynamic shapes while moving cohesively in the same direction. The main theoretical tools used to study the formation and dynamics of these shapes are so called self-propelled particle models. However, even the simplest models typically require computer simulations for their analysis, especially when the number of particles is small. For example, this is the case for the local attraction model with a blind angle. Here we explore three geometrical ideas based on transferring the attention from the particles themselves to the local center of mass they detect and the shapes they constitute. We use these methods to investigate the persistence and mobility of shapes in a local attraction model with a blind zone. More specifically, we address the persistence/stability of the mill shape. Then we investigate how the dynamics of the detected local center of mass relate to the shapes we observe, including a moving figure of eight shape generated by the model.  Finally, we provide some insight into why some rotating chains exhibit translational motion and some do not. Although this work is in its infancy we believe that these ideas have potential and may facilitate analysis of similarly complex models.

National Category
Other Mathematics
Identifiers
urn:nbn:se:uu:diva-205884 (URN)
Available from: 2013-09-03 Created: 2013-08-23 Last updated: 2013-09-03
4. Solving the shepherding problem: Heuristics for herding autonomous, interacting agents
Open this publication in new window or tab >>Solving the shepherding problem: Heuristics for herding autonomous, interacting agents
Show others...
2014 (English)In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 11, no 100, 20140719- p.Article in journal (Refereed) Published
Abstract [en]

Herding of sheep by dogs is a powerful example of one individual causing many unwilling individuals to move in the same direction. Similar phenomena are central to crowd control, cleaning the environment and other engineering problems. Despite single dogs solving this 'shepherding problem' every day, it remains unknown which algorithm they employ or whether a general algorithm exists for shepherding. Here, we demonstrate such an algorithm, based on adaptive switching between collecting the agents when they are too dispersed and driving them once they are aggregated. Our algorithm reproduces key features of empirical data collected from sheep-dog interactions and suggests new ways in which robots can be designed to influence movements of living and artificial agents.

National Category
Ecology Other Mathematics
Identifiers
urn:nbn:se:uu:diva-205889 (URN)10.1098/rsif.2014.0719 (DOI)000341383000016 ()
Available from: 2013-09-03 Created: 2013-08-23 Last updated: 2017-12-06Bibliographically approved
5. Self-organized traffic via priority rules in leaf-cutting ants Atta colombica
Open this publication in new window or tab >>Self-organized traffic via priority rules in leaf-cutting ants Atta colombica
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Ants, termites and humans often form well-organized and highly efficient trails between different locations. Yet the microscopic traffic rules responsible for this organization and efficiency are not fully understood. Recent experimental work with leaf-cutting ants (Atta colombica) on a very narrow trail has suggested a set of priority rules thought to govern the traffic dynamics. Here we implement an agent-based model to investigate the sufficiency of these rules with respect to producing the observed spatio-temporal properties of the traffic. We compare the model results to four statistics of the real ant flow and find that they share several key characteristics. Then we extend the model to a wider trail and compare the simulation results with new experimental data from this setting. We find that the extended model is able to reproduce the general features of the flow seen in the experiments, including the formation of three-lane traffic. The experimental finding that Atta colombica indeed organize the flow into three-lane traffic is important in its own right and contradicts the previously held belief that Atta in general do not. Due to the simplicity of the proposed rules we believe that they may be responsible for organizing the traffic flow on trails in other species of ant, and perhaps even other trail forming animals such as termites and humans.

National Category
Ecology Other Mathematics
Identifiers
urn:nbn:se:uu:diva-205897 (URN)
Available from: 2013-09-03 Created: 2013-08-23 Last updated: 2013-09-03

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