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Related papers: Flocking of the Cucker-Smale and Motsch-Tadmor mod…

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In this chapter, we present the Cucker-Smale type flocking models, and discuss their mathematical structures and flocking theorems in terms of coupling strength, interaction topologies and initial data. In 2007, two mathematicians Felipe…

Analysis of PDEs · Mathematics 2016-04-19 Young-Pil Choi , Seung-Yeal Ha , Zhuchun Li

We present a sufficient condition of the complete position flocking theorem for the Cucker-Smale type model on the unit sphere with an inter-particle bonding force. For this second order dynamical system derived in [Choi, S.-H., Kwon, D.…

Dynamical Systems · Mathematics 2021-01-05 Sun-Ho Choi , Dohyun Kwon , Hyowon Seo

In this paper, we deal with a Cucker-Smale model with time-dependent time delay and communication failures. Namely, we investigate the situation in which the agents involved in a flocking process can possibly suspend the exchange of…

Optimization and Control · Mathematics 2025-08-19 Elisa Continelli

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

In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [12].Unlike…

Analysis of PDEs · Mathematics 2021-02-10 Roberto Natalini , Thierry Paul

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 introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the…

Analysis of PDEs · Mathematics 2015-05-27 Sebastien Motsch , Eitan Tadmor

We study the emergent behaviors of the weak solutions to the kinetic Cucker-Smale (in short, KCS) model in a non-compact spatial-velocity support setting. Unlike the compact support situation, non-compact support of a weak solution can…

Analysis of PDEs · Mathematics 2026-04-21 Seung-Yeal Ha , Xinyu Wang

This paper addresses the leader-follower flocking problem with a moving leader for networked Lagrange systems with parametric uncertainties under a proximity graph. Here a group of followers move cohesively with the moving leader to…

Optimization and Control · Mathematics 2015-07-23 Sheida Ghapani , Jie Mei , Wei Ren , Yongduan Song

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

The generic alignment conjecture states that for almost every initial data on the torus solutions to the Cucker-Smale system with a strictly local communication align to the common mean velocity. In this note we present a partial resolution…

Dynamical Systems · Mathematics 2025-08-12 Roman Shvydkoy

We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler…

Analysis of PDEs · Mathematics 2017-07-18 Young-Pil Choi , Jan Haskovec

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

Classical swarm models, exemplified by the Cucker--Smale framework, provide foundational insights into collective alignment but exhibit fundamental limitations in capturing the adaptive, heterogeneous behaviours intrinsic to living systems.…

Adaptation and Self-Organizing Systems · Physics 2025-09-08 Rene Fabregas , Jie Liao , Nisrine Outada

The study of collective behavior in multi-agent systems has attracted the attention of many researchers due to its wide range of applications. Among them, the Cucker-Smale model was developed to study the phenomenon of flocking, and various…

Dynamical Systems · Mathematics 2023-08-31 Jong-Ho Kim , Young Ju Lee , Jea-Hyun Park

We study finite-time flocking for an infinite set of Cucker-Smale particles with sublinear velocity coupling under fixed and switching sender networks. For this, we use a component-wise diameter framework and exploit sub-linear dissipation…

Dynamical Systems · Mathematics 2026-02-13 Seung-Yeal Ha , Xinyu Wang , Fanqin Zeng

We consider the celebrated Cucker-Smale model in finite dimension, modelling interacting collective dynamics and their possible evolution to consensus. The objective of this paper is to study the effect of time delays in the general model.…

Optimization and Control · Mathematics 2017-07-27 Cristina Pignotti , Emmanuel Trélat

For the discrete Cucker-Smale's flocking model with a singular communication weight $\psi(s) = s^{-\alpha}$, with $0<\alpha<1/2$ , we prove that the velocity component of certain type of weak solutions is absolutly continuous. This result…

Analysis of PDEs · Mathematics 2014-12-22 Jan Peszek

We study the effects of animal social networks with a weighted pattern of interactions on the flocking transition exhibited by models of self-organized collective motion. Considering a model representing dynamics on a one-dimensional…

Physics and Society · Physics 2022-10-19 Jaume Ojer , Romualdo Pastor-Satorras

We study the classical Cucker-Smale model in continuous time with a positive time delay $\tau$. As in the non-delayed case, unconditional flocking occurs when $\beta \leq 1/2$ for every $\tau>0$. Furthermore, we prove the exponential decay…

Analysis of PDEs · Mathematics 2020-08-24 Mauro Rodriguez Cartabia