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Related papers: Local well-posedness of the generalized Cucker-Sma…

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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

We first prove the well-posedness of weak and strong solutions to the kinetic Cucker-Smale model in the Sobolev space with the initial data having compact velocity support. Then we study the kinetic Cucker-Smale model with noise. By…

Analysis of PDEs · Mathematics 2017-04-25 Chunyin Jin

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

Consider a system of autonomous interacting agents moving in space, adjusting each own velocity as a weighted mean of the relative velocities of the other agents. In order to test the robustness of the model, we assume that each pair of…

Probability · Mathematics 2014-05-05 Eduardo Canale , Federico Dalmao , Ernesto Mordecki , Max Souza

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 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 and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…

Optimization and Control · Mathematics 2017-10-04 Christoforos Somarakis , Evripidis Paraskevas , John S. Baras , Nader Motee

We first present a new stochastic version of the Cucker-Smale model of the emergent behavior in flocks in which the mutual communication between individuals is affected by random factor. Then, the existence and uniqueness of global solution…

Probability · Mathematics 2015-08-28 Ta Viet Ton , Nguyen Thi Hoai Linh , Atsushi Yagi

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

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

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 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

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

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

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

We discuss strong local and global well-posedness for the three-dimensional NLS equation with nonlinearity concentrated on $\mathbb{S}^2$. Precisely, local well-posedness is proved for any $C^2$ power-nonlinearity, while global…

Analysis of PDEs · Mathematics 2024-01-02 Domenico Finco , Lorenzo Tentarelli , Alessandro Teta

We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called "topological distance" in previous works), which is the number of intermediate…

Dynamical Systems · Mathematics 2015-06-12 Jan Haskovec

We present a simple proof of asymptotic consensus in the discrete Hegselmann-Krause model and flocking in the discrete Cucker-Smale model with renormalization and variable delay. It is based on convexity of the renormalized communication…

Dynamical Systems · Mathematics 2020-06-30 Jan Haskovec

A mathematical theory on flocking serves the foundation for several ubiquitous multi-agent phenomena in biology, ecology, sensor networks, economy, as well as social behavior like language emergence and evolution. Directly inspired by the…

Populations and Evolution · Quantitative Biology 2007-05-23 Jackie , Shen