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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

Physical interactions generally respect certain symmetries, such as reciprocity and energy conservation, which survive in coarse grained isothermal descriptions. Active many-body systems usually break such symmetries intrinsically, on the…

Soft Condensed Matter · Physics 2022-08-31 Daniel Geiß , Klaus Kroy , Viktor Holubec

The aerial flocking of birds, or murmurations, has fascinated observers while presenting many challenges to behavioral study and simulation. We examine how the periphery of murmurations remain well bounded and cohesive. We also investigate…

Quantitative Methods · Quantitative Biology 2024-07-22 Rama Carl Hoetzlein

We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational…

Soft Condensed Matter · Physics 2016-01-20 Xingbo Yang , M. Cristina Marchetti

Collective motion is ubiquitous in nature; groups of animals, such as fish, birds, and ungulates appear to move as a whole, exhibiting a rich behavioral repertoire that ranges from directed movement to milling to disordered swarming.…

Adaptation and Self-Organizing Systems · Physics 2024-05-15 Conor Heins , Beren Millidge , Lancelot da Costa , Richard Mann , Karl Friston , Iain Couzin

Coordinated collective motion in bird flocks and fish schools inspires algorithms for cohesive swarm robotics. This paper presents a position-based flocking model that achieves persistent velocity alignment without velocity sensing. By…

Collective turns in starling flocks propagate linearly with negligible attenuation, indicating the existence of an underdamped sector in the dispersion relation. Beside granting linear propagation of the phase perturbations, the real part…

We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…

Statistical Mechanics · Physics 2012-08-16 Tamás Vicsek , Anna Zafeiris

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

Seminal works on animal collectives started proposing a diffusive model (overdamped) for the information transfer occurring in it \cite{Vicsek}. Afterwards, the introduction of self-rotational inertia brought into play an underdamped model…

Biological Physics · Physics 2026-04-28 Mario Sandoval

Living groups move in complex environments and are constantly subject to external stimuli, predatory attacks and disturbances. An efficient response to such perturbations is vital to maintain the group's coherence and cohesion.…

Statistical Mechanics · Physics 2023-04-12 Emanuele Loffredo , Davide Venturelli , Irene Giardina

Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena,…

Adaptation and Self-Organizing Systems · Physics 2015-06-04 Graciano Dieck Kattas , Xiao-ke Xu , Michael Small

We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing , Tadeusz Platkowski

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

Living entities in a group communicate and transfer information to one another for a variety of reasons. It might be for foraging food, migration, or escaping threats and obstacles, etc. They do so by interacting with each other and also…

Biological Physics · Physics 2024-04-03 Md. Samsuzzaman , Mohammad Hasanuzzaman , Ahmed Sayeed , Arnab Saha

Within a simple model of attractive active Brownian particles, we predict flocking behavior and challenge the widespread idea that alignment interactions are necessary to observe this collective phenomenon. Here, we show that even…

Soft Condensed Matter · Physics 2023-04-19 Lorenzo Caprini , Hartmut Löwen

Collective motion in animals and cells often exhibits rapid reorientations and scale-free velocity correlations. This allows information to spread rapidly through the group, allowing an adequate collective response to environmental changes…

Quantitative Methods · Quantitative Biology 2026-03-12 Simon Syga , Chandraniva Guha Ray , Josué Manik Nava-Sedeño , Fernando Peruani , Andreas Deutsch

Swarming is a conspicuous behavioural trait observed in bird flocks, fish shoals, insect swarms and mammal herds. It is thought to improve collective awareness and offer protection from predators. Many current models involve the hypothesis…

Quantitative Methods · Quantitative Biology 2015-06-22 Daniel J. G. Pearce , A. M. Miller , George Rowlands , Matthew S. Turner

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

Most of us must have been fascinated by the eye catching displays of collectively moving animals. Schools of fish can move in a rather orderly fashion and then change direction amazingly abruptly. There are a huge number of further examples…

Biological Physics · Physics 2011-01-13 K. Bhattacharya , Tamás Vicsek