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Related papers: Cucker-Smale type flocking models on a sphere

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In this paper, we propose a coupled system describing the interaction between the Relativistic Cucker-Smale model and the incompressible Navier-Stokes equations via a drag force, and establish a global existence theory as well as the…

Analysis of PDEs · Mathematics 2025-03-18 Shenglun Yan , Weiyuan Zou

We present an emergent stochastic flocking dynamics of the Cucker-Smale (CS) ensemble under randomly switching topologies. The evolution of the CS ensemble with randomly switching topologies involves two random components (switching times…

Optimization and Control · Mathematics 2019-11-19 Jiu-Gang Dong , Seung-Yeal Ha , Jinwook Jung , Doheon Kim

We prove existence of global $C^1$ piecewise weak solutions for the discrete Cucker-Smale's flocking model with the communication weight $\psi(s)=s^{-\alpha}, 0<\alpha<1.$ We also discuss the possibility of finite in time alignment of the…

Analysis of PDEs · Mathematics 2013-02-19 Jan Peszek

We study emergent behaviors of thermomechanical Cucker-Smale (TCS) ensemble confined in a harmonic potential field. In the absence of external force field, emergent dynamics of TCS particles has been extensively studied recently under…

Analysis of PDEs · Mathematics 2021-10-25 Hangjun Cho , Linglong Du , Seung-Yeal Ha

We consider the Cucker-Smale system with multiplicative noise in a harmonic potential field and investigate the effect of harmonic potential field. In the presence of external potential force, the system is expected to emerge into almost…

Dynamical Systems · Mathematics 2022-05-27 Du Linglong , Zhou Xinyun

We prove the existence of weak solutions to kinetic flocking model with cut-off interaction function by using Schauder fixed pointed theorem and velocity averaging lemma. Under the natural assumption that the velocity support of the initial…

Analysis of PDEs · Mathematics 2015-10-07 Chunyin Jin

In this paper, we revisit an interaction problem of two homogeneous Cucker-Smale (in short C-S) ensembles with attractive-repulsive couplings, possibly under the effect of Rayleigh friction, and study three sufficient frameworks leading to…

Dynamical Systems · Mathematics 2021-10-05 Di Fang , Seung-Yeal Ha , Shi Jin

In two recent papers the authors study the existence of weak solutions and the hydrodynamic limit of kinetic flocking equations with strong local alignment. The introduction of a strong local alignment term to model flocking behavior was…

Analysis of PDEs · Mathematics 2012-02-21 Trygve Karper , Antoine Mellet , Konstantina Trivisa

We study the invariance of velocity angles and flocking properties of the Inertial Spin model introduced by Cavagna et al. [J. Stat. Phys., 158, (2015), 601--627]. We present a novel approach, based on a second order nonlinear Gronwall…

Dynamical Systems · Mathematics 2021-10-28 Ioannis Markou

We provide a bird's eye view on developments in analyzing the long time, large crowd behavior of Cucker-Smale alignment dynamics. We consider a class of (fully-)discrete models, paying particular attention to general alignment protocols in…

Dynamical Systems · Mathematics 2023-06-06 Eitan Tadmor

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

We establish sufficient conditions for the quick relaxation to kinetic equilibrium in the classic Vicsek-Cucker-Smale model of bird flocking. The convergence time is polynomial in the number of birds as long as the number of flocks remains…

Multiagent Systems · Computer Science 2022-07-04 Bernard Chazelle , Kritkorn Karntikoon

Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group…

We investigate the hydrodynamic limit problem for a kinetic flocking model. We develop a GCI-based Hilbert expansion method, and establish rigorously the asymptotic regime from the kinetic Cucker-Smale model with a confining potential in a…

Analysis of PDEs · Mathematics 2025-08-26 Ning Jiang , Yi-Long Luo , Teng-Fei Zhang

We propose a second-order multi-agent system for target tracking on a sphere. The model contains a centripetal force, a bonding force, a velocity alignment operator to the target, and cooperative control between flocking agents. We propose…

Dynamical Systems · Mathematics 2021-07-12 Sun-Ho Choi , Dohyun Kwon , Hyowon Seo

This paper considers a group of mobile autonomous agents moving in Euclidean space with point mass dynamics. We introduce a set of coordination control laws that enable the group to generate the desired stable flocking motion. The control…

Statistics Theory · Mathematics 2007-06-13 Long Wang

The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…

Statistical Mechanics · Physics 2015-01-12 Illes J. Farkas , Jeromos Kun , Yi Jin , Gaoqi He , Mingliang Xu

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

We study emergent dynamics of the discrete Cucker-Smale (in short, DCS) model with randomly switching network topologies. For this, we provide a sufficient framework leading to the stochastic flocking with probability one. Our sufficient…

Dynamical Systems · Mathematics 2019-12-30 Jiu-Gang Dong , Seung-Yeal Ha , Jinwook Jung , Doheon Kim

We prove existence and uniqueness of strong solutions to the Cucker--Smale flocking model coupled with an incompressible viscous non-Newtonian fluid, with the stress tensor of a power--law structure for $p\geq\frac{11}{5}$. The coupling is…

Analysis of PDEs · Mathematics 2017-02-24 Piotr B. Mucha , Jan Peszek , Milan Pokorny