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We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $\phi$ and a non-linear coupling of velocities given by the power…

Analysis of PDEs · Mathematics 2026-01-01 Vinh Nguyen , Roman Shvydkoy , Changhui Tan

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 consider a particle system with a mean-field-type interaction perturbed by some common and individual noises. When the interacting kernels are sublinear and only locally Lipschitz-continuous, relying on arguments based on the tightness…

Probability · Mathematics 2020-07-27 Angelo Rosello

We consider aligning self-propelled particles in two dimensions. Their motion is given by generalized Langevin equations and includes non-additive N-particle interactions. The qualitative behavior is as for the famous Vicsek model. We…

Soft Condensed Matter · Physics 2021-09-08 Rüdiger Kürsten , Thomas Ihle

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

In this work, we perform modulation analysis of monokinetic limits from the kinetic Cucker- Smale model to the pressureless Euler alignment system. Two regimes are considered -- a strong Fokker- Planck force with vanishing noise and Knudsen…

Analysis of PDEs · Mathematics 2025-08-08 Alina Chertock , Roman Shvydkoy , Trevor Teolis

In this paper, we study limit behaviors of stationary measures of the Fokker-Planck equations associated with a system of ordinary differential equations perturbed by a class of multiplicative including additive white noises. As the noises…

Dynamical Systems · Mathematics 2016-07-22 Wen Huang , Min Ji , Zhenxin Liu , Yingfei Yi

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

We study a variant of the Cucker-Smale system with reaction-type delay. Using novel backward-forward and stability estimates on appropriate quantities we derive sufficient conditions for asymptotic flocking of the solutions. These…

Classical Analysis and ODEs · Mathematics 2025-10-03 Jan Haskovec , Ioannis Markou

In this paper, we discuss the flocking phenomenon for the Cucker-Smale and Motsch-Tadmor models in continuous time on a general oriented and weighted graph with a general communication function. We present a new approach for studying this…

Probability · Mathematics 2022-08-05 Adrien Jean Cotil

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…

Biological Physics · Physics 2016-03-02 Roberto de la Cruz , Pilar Guerrero , Fabian Spill , Tomás Alarcón

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

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 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 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

We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov-Fokker-Planck type of kinetic mean-field equation from the corresponding…

Analysis of PDEs · Mathematics 2017-05-12 Young-Pil Choi , Samir Salem

We study the kinetic Fokker-Planck equation perturbed by a stochastic Vlasov force term. When the noise intensity is not too large, we solve the Cauchy Problem in a class of well-localized (in velocity) functions. We also show that, when…

Analysis of PDEs · Mathematics 2017-06-20 Sylvain De Moor , Julien Vovelle , Luis Miguel Rodrigues

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 purpose of this paper is to consider flocking formations of a second order dynamic system on a sphere with a Cucker-Smale type flocking operator and cooperative control. The flocking operator consists of a weighted control parameter and…

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

We study the long time behaviour of the kinetic Fokker-Planck equation with mean field interaction, whose limit is often called Vlasov-Fkker-Planck equation. We prove a uniform (in the number of particles) exponential convergence to…

Analysis of PDEs · Mathematics 2019-12-06 Arnaud Guillin , Wei Liu , Liming Wu , Chaoen Zhang