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Related papers: Flocking in the Cucker-Smale model with self-delay…

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In this paper, we deal with first and second-order alignment models with non-universal interaction, time delay and possible lack of connection between the agents. More precisely, we analyze the situation in which the system's agents do not…

Optimization and Control · Mathematics 2025-08-26 Chiara Cicolani , Elisa Continelli , Cristina Pignotti

We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…

Analysis of PDEs · Mathematics 2026-02-17 Ruicheng Cheng , Seung-Yeal Ha , Jaemoon Lee , Zhenfu Wang

Collision avoidance is an interesting feature of the Cucker-Smale (CS) model of flocking that has been studied in many works, e.g. [1, 2, 4, 6, 7, 20, 21, 22]. In particular, in the case of singular interactions between agents, as is the…

Classical Analysis and ODEs · Mathematics 2018-07-03 Ioannis Markou

In particle systems, flocking refers to the phenomenon where particles' individual velocities eventually align. The Cucker-Smale model is a well-known mathematical framework that describes this behavior. Many continuous descriptions of the…

Analysis of PDEs · Mathematics 2024-07-29 Sebastian Zimper , Federico Cornalba , Nataša Djurdjevac Conrad , Ana Djurdjevac

We study the Cucker--Smale (C-S) flocking systems involving both singularity and noise. We first show the local strong well-posedness for the stochastic singular C-S systems before the first collision time, which is a well defined stopping…

Dynamical Systems · Mathematics 2021-09-21 Qiao Huang , Xiongtao Zhang

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…

Analysis of PDEs · Mathematics 2019-02-01 P. Aceves-Sánchez , M. Bostan , J. A. Carrillo , P. Degond

In this paper, we study a continuous ocking Cucker-Smale model with noise, which has isotropic and polarized stationary solutions depending on the intensity of the noise. The first result establishes the threshold value of the noise…

Analysis of PDEs · Mathematics 2024-05-13 Xingyu Li

We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We…

Analysis of PDEs · Mathematics 2019-05-22 Javier Morales , Jan Peszek , Eitan Tadmor

We present pathwise flocking dynamics and local sensitivity analysis for the Cucker-Smale(C-S) model with random communications and initial data. For the deterministic communications, it is well known that the C-S model can model emergent…

Dynamical Systems · Mathematics 2017-12-13 Seung-Yeal Ha , Shi Jin

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 discuss the Cucker-Smale's (C-S) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasov-type kinetic model for the C-S…

Analysis of PDEs · Mathematics 2008-06-16 Seung-Yeal Ha , Eitan Tadmor

We present a direct proof of asymptotic consensus in the nonlinear Hegselmann-Krause model with transmission-type delay, where the communication weights depend on the particle distance in phase space. Our approach is based on an explicit…

Dynamical Systems · Mathematics 2021-09-17 Jan Haskovec

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding…

Analysis of PDEs · Mathematics 2021-02-04 Piotr Minakowski , Piotr B. Mucha , Jan Peszek , Ewelina Zatorska

We study emergent behaviors of Cucker-Smale(CS) flocks on the hyperboloid $\mathbb{H}^d$ in any dimensions. In a recent work \cite{H-H-K-K-M}, a first-order aggregation model on the hyperboloid was proposed and its emergent dynamics was…

Mathematical Physics · Physics 2021-08-25 Hyunjin Ahn , Seung-Yeal Ha , Hansol Park , Woojoo Shim

We study a new flocking model which has the versatility to capture the physically realistic qualitative behavior of the Motsch-Tadmor model, while also retaining the entropy law, which lends to a similar 1D global well-posedness analysis to…

Analysis of PDEs · Mathematics 2024-06-14 Roman Shvydkoy , Trevor Teolis

We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a communication…

Adaptation and Self-Organizing Systems · Physics 2012-05-02 Luis Mier-y-Teran-Romero , Eric Forgoston , Ira B. Schwartz

We introduce a Vicsek-like flocking model with a minimal form of time-delayed orientational interactions, in which the delays occur on a time scale that is well-separated from other time scales in the model. We achieve this by implementing…

Soft Condensed Matter · Physics 2025-05-19 Charles R. Packard , Daniel M. Sussman

We present a new stochastic particle system on networks which describes the flocking behavior and pattern formation. More precisely, we consider Cucker-Smale particles with decentralized formation control and multiplicative noises on…

Dynamical Systems · Mathematics 2022-04-20 Young-Pil Choi , Doeun Oh , Oliver Tse

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 consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modelling. In the asymptotic regime of slow diffusion, that coincides…

Populations and Evolution · Quantitative Biology 2017-02-17 Daniele De Martino , Davide Masoero