Emergent behaviour in multi-particle systems with non-local interactions

Kolokolnikov, Théodore; Carrillo, José A.; Bertozzi, Andrea L.; Fetecau, Razvan C.; Lewis, Mark A.

doi:10.1016/j.physd.2013.06.011

Cited by 80 publications

(70 citation statements)

References 80 publications

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“…We end this paper with a brief discussion of the relationship between that work and ours. Any meaningful review of research on swarming would require a dedicated paper and we do not attempt it-as a good starting point the reader is referred to Kolokolnikov et al (2013) and to the special journal issue that this article introduces. The generic model for swarming is a version of (2), with D = 0, p(.)…”

Section: Discussionmentioning

confidence: 99%

A Nonlocal Model for Contact Attraction and Repulsion in Heterogeneous Cell Populations

et al. 2015

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Instructing others to move is fundamental for many populations, whether animal or cellular. In many instances, these commands are transmitted by contact, such that an instruction is relayed directly (e.g. by touch) from signaller to receiver: for cells, this can occur via receptor-ligand mediated interactions at their membranes, potentially at a distance if a cell extends long filopodia. Given that commands ranging from attractive to repelling can be transmitted over variable distances and between cells of the same (homotypic) or different (heterotypic) type, these mechanisms can clearly have a significant impact on the organisation of a tissue. In this paper, we extend a system of nonlocal partial differential equations (integrodifferential equations) to provide a general modelling framework to explore these processes, performing linear stability and numerical analyses to reveal its capacity to trigger the self-organisation of tissues. We demonstrate the potential of the framework via two illustrative applications: the contact-mediated dispersal of neural crest populations and the self-organisation of pigmentation patterns in zebrafish.

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Section: Discussionmentioning

confidence: 99%

A Nonlocal Model for Contact Attraction and Repulsion in Heterogeneous Cell Populations

et al. 2015

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“…Let us now investigate the same equation (22) but in the case of the space periodic domain. We will check an influence of the size of the domain on the stability of stationary solutions.…”

Section: Linear Analysis In the Spatially Periodic Casementioning

confidence: 99%

Kinetic Theory of Particle Interactions Mediated by Dynamical Networks

Barré¹,

Degond²,

Zatorska³

2017

Multiscale Model. Simul.

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Abstract. We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle and link densities, following the approach of [P. Degond, F. Delebecque, and D. Peurichard, Math. Models Methods Appl. Sci., 26 (2016), pp. 269-318]. Assuming that the process of remodeling the network is very fast, we simplify the description to a macroscopic model taking the form of a single aggregation-diffusion equation for the density of particles. We analyze qualitatively this equation, addressing the stability of a homogeneous distribution of particles for a general potential. For the Hookean potential we obtain a precise condition for the phase transition, and, using the central manifold reduction, we characterize the type of bifurcation at the instability onset.

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“…Kinetic models have been introduced in the last years for the mesoscopic description of collective behavior of agents/particles with applications in collective behavior of cell and animal populations, see [19,37,42] and the references therein for a general overview on this active field. These models usually include alignment, attraction and repulsion as basic bricks of interactions between individuals.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic limits for kinetic flocking models of Cucker-Smale type

Aceves-Sanchez¹,

Bostan²,

Carrillo³

et al. 2019

Mathematical Biosciences and Engineering

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We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The self-propelling and friction forces together with the alignment and the noise are interpreted as a collision/interaction mechanism acting with equal strength. We show that the set of generalized collision invariants, introduced in [29], is equivalent in our setting to the more classical notion of collision invariants, i.e., the kernel of a suitably linearized collision operator. After identifying these collision invariants, we derive the fluid model, by appealing to the balances for the particle concentration and orientation. We investigate the main properties of the macroscopic model for a general potential with radial symmetry.

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Emergent behaviour in multi-particle systems with non-local interactions

Cited by 80 publications

References 80 publications

A Nonlocal Model for Contact Attraction and Repulsion in Heterogeneous Cell Populations

A Nonlocal Model for Contact Attraction and Repulsion in Heterogeneous Cell Populations

Kinetic Theory of Particle Interactions Mediated by Dynamical Networks

Hydrodynamic limits for kinetic flocking models of Cucker-Smale type

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