Metric–topological interaction model of collective behavior

Niizato, Takayuki; Gunji, Yukio Pegio

doi:10.1016/j.ecolmodel.2011.06.008

Cited by 37 publications

(36 citation statements)

References 40 publications

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“…However, there has been recent compelling evidence [1] that interactions within bird flocks are mostly metric free, as the birds react primarily with a limited number of their nearest neighbours irrespective of the distances between them. This observation has motivated the concept of "topological interaction", which has been widely echoed in the scientific literature [5,7,10,13,19].…”

Section: Introductionmentioning

confidence: 99%

Topological Interactions in a Boltzmann-Type Framework

Blanchet

Degond

2016

J Stat Phys

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We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader according to the proximity rank of the latter with respect to the former. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit equation is akin to the Boltzmann equation. However, it exhibits a spatial non-locality instead of the classical non-locality in velocity space. This result relies on the approximation properties of Bernstein polynomials. We illustrate the dynamics with numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Topological Interactions in a Boltzmann-Type Framework

Blanchet

Degond

2016

J Stat Phys

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“…The onset of time-dependent patterns in our system (or dynamic emergence) is what makes our research different from previous studies. We have seen that particles aligning based on metric [6,22,24] and topological [18][19][20][21] interactions only give rise to stable structures like vortices or to time-dependent global alternating patterns (oscillatory and translational phases) [20]. Even with a different interaction rule like in Touma et al [25] where particles are coupled by an exponential potential, their system is able to self-organize and generate once again stable structures like rings, droplets, and polarized droplets.…”

Section: O M P L E X I T Ymentioning

confidence: 94%

“…They obtained a bistable region where the system may perform transitions between global oscillatory and translational phases. More recently, a study where interactions among birds are modeled as a mixture of topological and metric interactions has been reported by Niizato and Gunji [21].…”

Section: Boid Interactionsmentioning

confidence: 98%

Defining emergence: Learning from flock behavior

Berrondo

Sandoval

2015

Complexity

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The idea of emergence originates from the fact that global effects emerge from local interactions producing a collective coherent behavior. A particular instance of emergence is illustrated by a flocking model of interacting ''boids'' encompassing two antagonistic conducts-consensus and frustration-giving rise to highly complex, unpredictable, coherent behavior. The cohesive motion arising from consensus can be described in terms of three ordered dynamic phases. Once frustration is included in the model, local phases for specific groups of flockmates, and transitions among them, replace the global ordered phases. Following the evolution of boids in a single group, we discovered that the boids in this group will alternate among the three phases. When we compare two uncorrelated groups, the second group shows a similar behavior to the first one, but with a different sequence of phases. Besides the visual observation of our animations with marked boids, the result is evident plotting the local order parameters. Rather than adopting one of the consensus ordered phases, the flock motion resembles more an entangled dynamic sequence of phase transitions involving each group of flockmates. V C 2015 Wiley Periodicals, Inc. Complexity 000: 00-00, 2015

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“…Topological-based rules allow individuals to weigh information equally from a set number of near or distant neighbours while incorporating similar principles of attraction, repulsion and alignment [27]. …”

Section: Methodsmentioning

confidence: 99%

Collective behaviour in vertebrates: a sensory perspective

et al. 2016

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Collective behaviour models can predict behaviours of schools, flocks, and herds. However, in many cases, these models make biologically unrealistic assumptions in terms of the sensory capabilities of the organism, which are applied across different species. We explored how sensitive collective behaviour models are to these sensory assumptions. Specifically, we used parameters reflecting the visual coverage and visual acuity that determine the spatial range over which an individual can detect and interact with conspecifics. Using metric and topological collective behaviour models, we compared the classic sensory parameters, typically used to model birds and fish, with a set of realistic sensory parameters obtained through physiological measurements. Compared with the classic sensory assumptions, the realistic assumptions increased perceptual ranges, which led to fewer groups and larger group sizes in all species, and higher polarity values and slightly shorter neighbour distances in the fish species. Overall, classic visual sensory assumptions are not representative of many species showing collective behaviour and constrain unrealistically their perceptual ranges. More importantly, caution must be exercised when empirically testing the predictions of these models in terms of choosing the model species, making realistic predictions, and interpreting the results.

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Metric–topological interaction model of collective behavior

Cited by 37 publications

References 40 publications

Topological Interactions in a Boltzmann-Type Framework

Topological Interactions in a Boltzmann-Type Framework

Defining emergence: Learning from flock behavior

Collective behaviour in vertebrates: a sensory perspective

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