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We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $\phi$ and a non-linear coupling of velocities given by the power…

Analysis of PDEs · Mathematics 2026-01-01 Vinh Nguyen , Roman Shvydkoy , Changhui Tan

In this paper, we consider the Cucker-Smale flocking particles which are subject to the same velocity-dependent noise, which exhibits a phase change phenomenon occurs bringing the system from a "non flocking" to a "flocking" state as the…

Analysis of PDEs · Mathematics 2017-11-29 Young-Pil Choi , Samir Salem

In this paper, we present an innovative particle system characterized by moderate interactions, designed to accurately approximate kinetic flocking models that incorporate singular interaction forces and local alignment mechanisms. We…

Analysis of PDEs · Mathematics 2024-04-23 Jinhuan Wang , Keyu Li , Hui Huang

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 present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered - including examples for the widely observed behavior of hierarchically interacting…

Physics and Society · Physics 2019-04-23 Yongnan Jia , Tamas Vicsek

Over the past few decades, the research community has been interested in the study of multi-agent systems and their emerging collective dynamics. These systems are all around us in nature, like bacterial colonies, fish schools, bird flocks,…

Adaptation and Self-Organizing Systems · Physics 2023-12-12 Gourab Kumar Sar , Dibakar Ghosh

We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a…

Probability · Mathematics 2012-01-12 François Bolley , José Alfredo Cañizo , José Antonio Carrillo

We consider large but finite systems of identical agents on the line with up to next nearest neighbor asymmetric coupling. Each agent is modelled by a linear second order differential equation, linearly coupled to up to four of its…

Dynamical Systems · Mathematics 2021-07-23 J. Herbrych , A. G. Chazirakis , N. Christakis , J. J. P. Veerman

We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…

Statistical Mechanics · Physics 2013-12-03 Shamik Gupta , Thierry Dauxois , Stefano Ruffo

In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…

Dynamical Systems · Mathematics 2014-03-31 J. A. Carrillo , Y. Huang , S. Martin

Coherent collective motion is a widely observed phenomenon in active matter systems. Here, we report a flocking transition mechanism in a system of chemically interacting active colloidal particles sustained purely by chemo-repulsive…

Soft Condensed Matter · Physics 2025-11-04 Arvin Gopal Subramaniam , Sagarika Adhikary , Rajesh Singh

The mean-field dynamics of a collection of stochastic agents with local versus nonlocal interactions is studied via analytically soluble models. The nonlocal interactions result from a barycentric modulation of the observation range of the…

Adaptation and Self-Organizing Systems · Physics 2012-06-01 Max-Olivier Hongler , Roger Filliger , Olivier Gallay

Collective behavior is all around us, from flocks of birds to schools of fish. These systems are immensely complex, which makes it pertinent to study their behavior through minimal models. We introduce such a minimal model for cohesive and…

Soft Condensed Matter · Physics 2025-01-29 Jeanine Shea , Holger Stark

In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic…

Populations and Evolution · Quantitative Biology 2020-04-23 Jitesh Jhawar , Vishwesha Guttal

We provide evidence that for some values of the parameters a simple agent based model, describing herding behavior, yields signals with 1/f power spectral density. We derive a non-linear stochastic differential equation for the ratio of…

Adaptation and Self-Organizing Systems · Physics 2015-06-03 J. Ruseckas , B. Kaulakys , V. Gontis

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

We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen…

Statistical Mechanics · Physics 2026-04-23 Chunming Zheng

We characterize the dynamic non-equilibrium steady state behavior of active particles using density fluctuations in the system. We analyze the effective local density around a particle in the steady state and numerically calculate its mean,…

Statistical Mechanics · Physics 2025-04-22 Jayam Joshi , Pawan Kumar Mishra , Shradha Mishra

The flocking of self-propelled particles in heterogeneous environments is relevant to both natural and artificial systems. The Vicsek model is a canonical choice to investigate such systems due to the minimal number of parameters required…

Computational Physics · Physics 2024-12-11 Eighdi Aung , Nicole Abaid , James E. McClure

We consider the Czir\'ok model for collective motion of locusts along a one-dimensional torus. In the model, each agent's velocity locally interacts with other agents' velocities in the system, and there is also exogenous randomness to each…

Analysis of PDEs · Mathematics 2018-03-12 Josselin Garnier , George Papanicolaou , Tzu-Wei Yang