Noise-induced transition from translational to rotational motion of swarms

Erdmann, Udo; Ébeling, W.; Mikhailov, Alexander S.

doi:10.1103/physreve.71.051904

Cited by 147 publications

(154 citation statements)

References 40 publications

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“…Models with only attractive and repulsive interactions have long been studied in biology in the context of group formation and swarming [26 -28]. Still, only relatively few models have focused on the onset of collective motion without alignment based on purely repulsive and attractive interactions [29][30][31][32][33][34]. This is most probably because velocity alignment provides a simple and robust mechanism for the onset of polarized swarms, where individuals are able to agree on a common direction of motion.…”

Section: Introductionmentioning

confidence: 99%

“…One contribution of 11 to a Theme Issue 'Collective motion in biological systems: experimental approaches joint with particle and continuum models '. self-propelled agents [30,33,35]. Although this 'physical' mechanisms yield very interesting results and can lead to coordinated motion of individual units, they are most probably not suited to explain the dynamics of many biological systems.…”

Section: Introductionmentioning

confidence: 99%

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Swarming and pattern formation due to selective attraction and repulsion

Romanczuk

Schimansky‐Geier

2012

Interface Focus.

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We discuss the collective dynamics of self-propelled particles with selective attraction and repulsion interactions. Each particle, or individual, may respond differently to its neighbours depending on the sign of their relative velocity. Thus, it is able to distinguish approaching (coming closer) and retreating (moving away) individuals. This differentiation of the social response is motivated by the response to looming visual stimuli and may be seen as a generalization of the previously proposed escape and pursuit interactions motivated by empirical evidence for cannibalism as a driving force of collective migration in locusts and Mormon crickets. The model can account for different types of behaviour such as pure attraction, pure repulsion or escape and pursuit, depending on the values (signs) of the different response strengths. It provides, in the light of recent experimental results, an interesting alternative to previously proposed models of collective motion with an explicit velocity -alignment interaction. We discuss the derivation of a coarse-grained description of the system dynamics, which allows us to derive analytically the necessary condition for emergence of collective motion. Furthermore, we analyse systematically the onset of collective motion and clustering in numerical simulations of the model for varying interaction strengths. We show that collective motion arises only in a subregion of the parameter space, which is consistent with the analytical prediction and corresponds to an effective escape and/or pursuit response.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Swarming and pattern formation due to selective attraction and repulsion

Romanczuk

Schimansky‐Geier

2012

Interface Focus.

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“…The formulations to study the flocking phenomenon can be succinctly classified in rule-based [10,11,12,13,14,15,16,17,18], Lagrangian (trajectory-based) [19,20,21,22,23,24,25,26] and Eulerian (continuum) models [27,28,29]. Regarding the dimensionality of the models developed, most of them have been defined in dimensions higher than one [10,11,12,13,14,15,20,21,22,23,24,25,27,28,29,30], since the velocity of the self-propelled particles (SPP) in these models can have continuous values. In contrast, only a few one-dimensional (1D) models have been studied [5,16,17,18,19,26,31].…”

Section: Introductionmentioning

confidence: 99%

Cohesive motion in one-dimensional flocking

Dossetti¹

2011

J. Phys. A: Math. Theor.

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Abstract. A one-dimensional rule-based model for flocking, that combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to a unique group behaviour that contrasts with previous studies. Our results show that the largest cluster of particles, in the condensed states, develops a mean velocity slower than the preferred one in the absence of noise. For strong noise, the system also develops a non-vanishing mean velocity, alternating its direction of motion stochastically. This allows us to address the directional switching phenomenon. The effects of different sources of stochasticity on the system are also discussed.

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“…Here we concentrate on a further simplification in which we use just one term for social interactions, namely local attraction. SPP models with global attraction as the only interaction produce a range of dynamic structures, some of which produce dynamic moving patterns (Mikhailov et al, 1999;Erdmann et al, 2005;Ebeling et al, 2008). Here we concentrate on a minimal model in which we use local attraction.…”

Section: Introductionmentioning

confidence: 99%

Collective motion from local attraction

Strömbom

2011

Journal of Theoretical Biology

126

149

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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.

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Noise-induced transition from translational to rotational motion of swarms

Cited by 147 publications

References 40 publications

Swarming and pattern formation due to selective attraction and repulsion

Swarming and pattern formation due to selective attraction and repulsion

Cohesive motion in one-dimensional flocking

Collective motion from local attraction

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