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Flocks of starlings exhibit a remarkable ability to maintain cohesion as a group in highly uncertain environments and with limited, noisy information. Recent work demonstrated that individual starlings within large flocks respond to a fixed…

Populations and Evolution · Quantitative Biology 2013-02-14 George Forrest Young , Luca Scardovi , Andrea Cavagna , Irene Giardina , Naomi Ehrich Leonard

Several models of flocking have been promoted based on simulations with qualitatively naturalistic behavior. In this paper we provide the first direct application of computational modeling methods to infer flocking behavior from…

Other Quantitative Biology · Quantitative Biology 2015-05-30 Graciano Dieck Kattas , Xiao-Ke Xu , Michael Small

We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…

Statistical Mechanics · Physics 2019-07-24 Trilochan Bagarti , Shakti N. Menon

Animals that travel together in groups display a variety of fascinating motion patterns thought to be the result of delicate local interactions among group members. Although the most informative way of investigating and interpreting…

Biological Physics · Physics 2010-10-27 Mate Nagy , Zsuzsa Akos , Dora Biro , Tamas Vicsek

Collective decision-making in biological systems requires all individuals in the group to go through a behavioural change of state. During this transition, the efficiency of information transport is a key factor to prevent cohesion loss and…

From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behaviour have aimed to understand how a globally ordered state may emerge from simple…

Populations and Evolution · Quantitative Biology 2014-10-10 Andrea Cavagna , Alessio Cimarelli , Irene Giardina , Giorgio Parisi , Raffaele Santagati , Fabio Stefanini , Massimiliano Viale

Consider a flock of birds that fly interacting between them. The interactions are modelled through a hierarchical system in which each bird, at each time step, adjusts its own velocity according to his past velocity and a weighted mean of…

Probability · Mathematics 2009-12-24 Federico Dalmao , Ernesto Mordecki

The most conspicuous trait of collective animal behaviour is the emergence of highly ordered structures. Less obvious to the eye, but perhaps more profound a signature of self-organization, is the presence of long-range spatial…

Soft Condensed Matter · Physics 2013-04-24 Andrea Cavagna , Irene Giardina , Francesco Ginelli

Large animal groups -- bird flocks, fish schools, insect swarms -- are often assumed to form by gradual aggregation of sparsely distributed individuals. Using a mathematically precise framework based on time-varying directed interaction…

Populations and Evolution · Quantitative Biology 2025-12-02 Jidong Jin

Flocking, as paradigmatically exemplified by birds, is the coherent collective motion of active agents. As originally conceived, flocking emerges through alignment interactions between the agents. Here, we report that flocking can also…

Soft Condensed Matter · Physics 2024-07-16 Suchismita Das , Matteo Ciarchi , Ziqi Zhou , Jing Yan , Jie Zhang , Ricard Alert

We study a model of flocking in order to describe the transitions during the collective motion of organisms in three dimensions (e.g., birds). In this model the particles representing the organisms are self-propelled, i.e., they move with…

Biological Physics · Physics 2015-06-26 A. Czirok , M. Vicsek , T. Vicsek

We investigate the emergence of cohesive flocking in open, boundless space using a multi-agent reinforcement learning framework. Agents integrate positional and orientational information from their closest topological neighbours and learn…

Soft Condensed Matter · Physics 2026-02-02 Martino Brambati , Antonio Celani , Marco Gherardi , Francesco Ginelli

Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where…

Adaptation and Self-Organizing Systems · Physics 2012-01-16 Nicholas A. Mecholsky , Edward Ott , Thomas M. Antonsen , Parvez Guzdar

We formulate a kinetic theory of two species of hard spheres undergoing reactive collisions that convert chemical energy into kinetic energy. The model describes an active species interacting with a passive background, labeled as birds and…

Statistical Mechanics · Physics 2026-01-07 Ruben Lier

Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the…

Biological Physics · Physics 2024-06-04 Vijay Kumar , Rumi De

As the constituents of a flock are polar, one expects a fore-aft asymmetry in their interactions. We show here that the resulting antisymmetric part of the "exchange coupling" between a bird and its neighbours, if large enough, destabilizes…

Statistical Mechanics · Physics 2020-05-06 Lokrshi Prawar Dadhichi , Rahul Chajwa , Ananyo Maitra , Sriram Ramaswamy

Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors,…

Quantitative Methods · Quantitative Biology 2026-01-23 Yogesh Kumar KC , Arshed Nabeel , Srikanth Iyer , Vishwesha Guttal

Animal swarms displaying a variety of typical flocking patterns would not exist without underlying safe, optimal and stable dynamics of the individuals. The emergence of these universal patterns can be efficiently reconstructed with…

Adaptation and Self-Organizing Systems · Physics 2015-06-17 Csaba Virágh , Gábor Vásárhelyi , Norbert Tarcai , Tamás Szörényi , Gergő Somorjai , Tamás Nepusz , Tamás Vicsek

When particles move at a constant speed and have the tendency to align their directions of motion, ordered large scale movement can emerge despite significant levels of noise. Many variants of this model of self-propelled particles have…

Biological Physics · Physics 2012-12-11 Matthias Meschede , Oskar Hallatschek

Aligning self-propelled particles undergo a nonequilibrium flocking transition from apolar to polar phases as their interactions become stronger. We propose a thermodynamically consistent lattice model, in which the internal state of the…

Statistical Mechanics · Physics 2025-08-08 Karel Proesmans , Gianmaria Falasco , Atul Tanaji Mohite , Massimiliano Esposito , Étienne Fodor