Asymptotic flocking for the three-zone model

Cao, Fei; Motsch, Sébastien; Reamy, Alexander; Theisen, Ryan

doi:10.3934/mbe.2020391

Cited by 4 publications

(7 citation statements)

References 35 publications

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“…In spp models a number of particles move and interact with nearby particles via a set of local interaction rules, for example, attraction, repulsion, and alignment [2,4]. Models including these three interactions have been shown to generate the standard groups: mills, swarms, and aligned (or polarized or dynamic) groups [4,5], and have been widely adopted in modeling collective motion in specific real animal groups (e.g., [6,7]) and as base models for general theoretical investigations (e.g., [8,9]). The capacity of these models to produce group level alignment via the explicit alignment interaction has been critical in modeling groups of animals that move collectively through the environment.…”

Section: Introductionmentioning

confidence: 99%

Attraction vs. Alignment as Drivers of Collective Motion

Strömbom

Tulevech

2022

Front. Appl. Math. Stat.

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Moving animal groups exhibit a range of fascinating behaviors. The standard explanation for how these groups form and function is that the individual animals interact via attraction, repulsion, and alignment, where alignment is proposed to drive the collective motion. However, it has been shown both experimentally and theoretically that alignment interactions are not required to induce group level alignment. In particular, via the use of self-propelled particle models it has been established that several other mechanisms induce group level alignment (aka polarization) in combination with attraction alone. However, no systematic comparison of these mechanisms among themselves, or with explicit alignment, has been presented and it remains unclear how, or even if, they can be distinguished at the collective level. Here, we introduce two previously unreported mechanisms, burst-and-glide and burst-and-stop, and show via simulation that they also induce polarization in combination with attraction alone. Then, we compare the polarization inducing characteristics of six mechanisms; asymmetric interactions, asynchrony, anticipation, burst-and-glide, burst-and stop, and explicit alignment. We show that the mechanisms induce polarization in different parts of the attraction parameter space, that the route to polarization from uniformly random initial conditions, as well as repolarization following strong perturbations, is markedly different among the mechanisms. In particular, we find that alignment based and non-alignment based mechanisms can be distinguished via their polarization and repolarization processes. These findings further challenge the current alignment based theory of collective motion and may contribute to a more versatile theory of collective motion across scales.

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Section: Introductionmentioning

confidence: 99%

Attraction vs. Alignment as Drivers of Collective Motion

Strömbom

Tulevech

2022

Front. Appl. Math. Stat.

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“…Given an agent-based model, one is expected to identify the limit dynamics as the number of individuals tends to infinity and then its corresponding equilibrium when run the model for a sufficiently long time (if there is one), and this guiding approach is carried out in numerous works across different fields among literatures of applied mathematics, see for instance. [10][11][12][13][14] In this work, we consider the so-called repeated averaging model for money exchange in a closed economic system with N agents. The dynamics consists of choosing at random time two individuals and to redistribute equally their combined wealth.…”

Section: Introductionmentioning

confidence: 99%

“…From a mathematical point of view, we have to understand the fundamental mechanisms, such as money exchange resulting from individuals, which are usually agent‐based models. Given an agent‐based model, one is expected to identify the limit dynamics as the number of individuals tends to infinity and then its corresponding equilibrium when run the model for a sufficiently long time (if there is one), and this guiding approach is carried out in numerous works across different fields among literatures of applied mathematics, see for instance 10–14 …”

Section: Introductionmentioning

confidence: 99%

Explicit decay rate for the Gini index in the repeated averaging model

Cao

2022

Math Methods in App Sciences

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We investigate the repeated averaging model for money exchanges: two agents picked uniformly at random share half of their wealth to each other. It is intuitively convincing that a Dirac distribution of wealth (centered at the initial average wealth) will be the long time equilibrium for this dynamics. In other words, the Gini index should converge to zero. To better understand this dynamics, we investigate its limit as the number of agents goes to infinity by proving the so-called propagation of chaos, which links the stochastic agent-based dynamics to a (limiting) nonlinear partial differential equation (PDE). This deterministic description has a flavor of the classical Boltzmann equation arising from statistical mechanics of dilute gases. We prove its convergence towards its Dirac equilibrium distribution by showing that the associated Gini index of the wealth distribution converges to zero with an explicit rate. KEYWORDS agent-based model, econophysics, Gini index, propagation of chaos, repeated averaging MSC CLASSIFICATION 91B80, 91B70

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“…All these models have stimulated an intense literature which is impossible to cite exhaustively (see e.g. [15] for the three-zone model, [19,21,27,28,38,41,43,46,52,63,66] for the Vicsek model, and [1,4,5,16,48,49,50] for the Cucker-Smale model). Variants or combinations of these different models can be found in [8,9,10,54].…”

Section: Introductionmentioning

confidence: 99%

“…Traditionally, there are three levels of modelling for systems of interacting agents. The finer level of description is the "particle" level, by which each agent is followed in the course of time by means of ordinary differential equations or stochastic processes [3,15,19,21,23,50,53,54,64]. This is an appealing approach as the behavioral rules can be directed encoded in the equations.…”

Section: Introductionmentioning

confidence: 99%

Body-attitude coordination in arbitrary dimension

Degond¹,

Diez²,

Frouvelle³

2021

Preprint

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We consider a system of self-propelled agents interacting through body attitude coordination in arbitrary dimension n ≥ 3. We derive the formal kinetic and hydrodynamic limits for this model. Previous literature was restricted to dimension n = 3 only and relied on parametrizations of the rotation group that are only valid in dimension 3. To extend the result to arbitrary dimensions n ≥ 3, we develop a different strategy based on Lie group representations and the Weyl integration formula. These results open the way to the study of the resulting hydrodynamic model (the "Self-Organized Hydrodynamics for Body orientation (SOHB)") in arbitrary dimensions.

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Asymptotic flocking for the three-zone model

Cited by 4 publications

References 35 publications

Attraction vs. Alignment as Drivers of Collective Motion

Attraction vs. Alignment as Drivers of Collective Motion

Explicit decay rate for the Gini index in the repeated averaging model

Body-attitude coordination in arbitrary dimension

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