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We investigate a Cucker-Smale-type flocking model for multi-agent systems that move with constant speed. The model incorporates both kinematic observables and internal energy (temperatures) in the agents' interactions. Traditionally,…

Classical Analysis and ODEs · Mathematics 2023-04-04 Hyunjin Ahn , Junhyeok Byeon , Seung-Yeal Ha

In this paper, we quantify the asymptotic limit of collective behavior kinetic equations arising in mathematical biology modeled by Vlasov-type equations with nonlocal interaction forces and alignment. More precisely, we investigate the…

Analysis of PDEs · Mathematics 2020-07-10 José A. Carrillo , Young-Pil Choi , Jinwook Jung

We investigate a continuum Lagrangian $p$-alignment system given by a nonlocal mean-field system of ordinary differential equations for interacting agents with weak initial data. We first establish global well-posedness of the Lagrangian…

Analysis of PDEs · Mathematics 2026-04-14 José A. Carrillo , Young-Pil Choi , Eitan Tadmor

The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency e.g. to aggregate, flock or disperse. The paper examines the kinetic…

Analysis of PDEs · Mathematics 2017-07-19 Piotr B. Mucha , Jan Peszek

In this work, we study the deterministic Cucker-Smale model with topological interaction. Focusing on the solutions of the corresponding Liouville equation, we show that propagation of chaos holds. Moreover, considering monokinetic…

Analysis of PDEs · Mathematics 2024-10-25 Dario Benedetto , Thierry Paul , Stefano Rossi

We introduce a multi-dimensional variant of the kinetic Cucker-Smale model with singular and matrix-valued communication weight, which reduces to the singular kinetic Cucker-Smale equation in the one-dimensional case. We propose an…

Analysis of PDEs · Mathematics 2022-08-01 Jan Peszek , David Poyato

We analyze the Cucker-Smale model under hierarchical leadership in presence of a time delay. By using a Lyapunov functional approach and some induction arguments we will prove convergence to consensus for every positive delay $\tau$. These…

Optimization and Control · Mathematics 2018-07-06 Cristina Pignotti , Irene Reche Vallejo

We study the Cucker-Smale model with a velocity control function. The Cucker-Smale model design the emergence of consensus in terms of flocking. A proposed model encompasses several Cucker-Smale models, such as a speed limit model, a…

Classical Analysis and ODEs · Mathematics 2023-02-08 Junhyeok Byeon

We investigate the large-time behavior of the pressureless Euler system with nonlocal velocity alignment and interaction forces, with the aim of characterizing the asymptotic convergence of classical solutions under general interaction…

Analysis of PDEs · Mathematics 2025-10-29 José A. Carrillo , Young-Pil Choi , Dowan Koo , Oliver Tse

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 present the relativistic analogue of the Cucker-Smale model with a bonding force on Riemannian manifold, and study its emergent dynamics. The Cucker-Smale model serves a prototype example of mechanical flocking models, and it has been…

Dynamical Systems · Mathematics 2023-01-19 Hyunjin Ahn , Junhyeok Byeon , Seung-Yeal Ha , Jaeyoung Yoon

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 study a variant of the Cucker-Smale model where information between agents propagates with a finite speed $\mathfrak{c}>0$. This leads to a system of functional differential equations with state-dependent delay. We prove that, if…

Analysis of PDEs · Mathematics 2021-12-28 Jan Haskovec

We present a new hydrodynamic model for synchronization phenomena which is a type of pressureless Euler system with nonlocal interaction forces. This system can be formally derived from the Kuramoto model with inertia, which is a classical…

Analysis of PDEs · Mathematics 2019-05-22 Young-Pil Choi , Jaeseung Lee

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 study a variant of the Cucker-Smale system with distributed reaction delays. Using backward-forward and stability estimates on the quadratic velocity fluctuations we derive sufficient conditions for asymptotic flocking of the solutions.…

Dynamical Systems · Mathematics 2020-05-12 Jan Haskovec , Ioannis Markou

We study the large-time behavior of Eulerian systems augmented with non-local alignment. Such systems arise as hydrodynamic descriptions of agent-based models for self-organized dynamics, e.g., Cucker-Smale and Motsch-Tadmor models…

Analysis of PDEs · Mathematics 2015-06-19 Eitan Tadmor , Changhui Tan

In this paper, we study sufficient conditions for the emergence of asymptotic consensus and flocking in a certain class of non-linear generalised Cucker-Smale systems subject to multiplicative communication failures. Our approach is based…

Optimization and Control · Mathematics 2021-05-04 Benoît Bonnet , Émilien Flayac

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 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