English
Related papers

Related papers: Flocking and non-flocking behavior in a stochastic…

200 papers

We analyze Cucker-Smale flocking particles with delayed coupling, where different constant delays are considered between particles. By constructing a system of dissipative differential inequalities together with a continuity argument, we…

Dynamical Systems · Mathematics 2017-12-05 Young-Pil Choi , Zhuchun Li

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

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

Flocking is ubiquitous in nature and emerges due to short- or long-range alignment interactions among self-propelled agents. Two unfriendly species that antialign or even interact nonreciprocally show more complex collective phenomena,…

Statistical Mechanics · Physics 2025-12-17 Jiwon Choi , Jae Dong Noh , Heiko Rieger

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 investigate the emergent behavior of four types of generic dynamical systems under random environmental perturbations. Sufficient conditions for nearly-emergence in various scenarios are presented. Recent fundamental works of F. Cucker…

Dynamical Systems · Mathematics 2019-09-18 Yilun Shang

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 how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…

Populations and Evolution · Quantitative Biology 2025-07-15 Alexandru Hening , Siddharth Sabharwal

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

When a collection of phenotypically diverse organisms compete with each other for limited resources, with competition being strongest amongst the most similar, the population can evolve into tightly localised clusters. This process can be…

Populations and Evolution · Quantitative Biology 2012-05-16 Tim Rogers , Alan J. McKane , Axel G. Rossberg

A one-dimensional rule-based model for flocking, that combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to a unique…

Statistical Mechanics · Physics 2015-01-19 V. Dossetti

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 present some recent development in modeling concurrent emergence of collective behaviors, namely, the emergence of clustering, flocking and synchronization at the same time. We derive two new models, namely Swarmalator-Vicsek and…

Dynamical Systems · Mathematics 2023-02-15 Trenton Gerew , Ming Zhong

We derive a sufficient condition for asymptotic flocking in the Cucker-Smale model with self-delay (also called reaction delay) and with non-symmetric interaction weights. The condition prescribes smallness of the delay length relative to…

Analysis of PDEs · Mathematics 2021-10-20 Jan Haskovec

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 present a stochastic version of the Cucker-Smale flocking dynamics based on a markovian $N$-particle system of pair interactions with unbounded and, in general, non-Lipschitz continuous interaction potential. We establish the infinite…

Probability · Mathematics 2022-03-17 Martin Friesen , Oleksandr Kutoviy

This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic…

Populations and Evolution · Quantitative Biology 2020-08-05 Almaz Tesfay , Daniel Tesfay , James Brannan , Jinqiao Duan

We consider the Cucker-Smale flocking model with a singular communication weight $\psi(s) = s^{-\alpha}$ with $\alpha > 0$. We provide a critical value of the exponent $\alpha$ in the communication weight leading to global regularity of…

Dynamical Systems · Mathematics 2016-09-13 Jose A. Carrillo , Young-Pil Choi , Piotr B. Mucha , Jan Peszek

We extend the analysis developed in [33] in order to prove convergence to consensus results for a Cucker-Smale type model with hierarchical leadership and distributed delay. Flocking estimates are obtained for a general interaction…

Optimization and Control · Mathematics 2018-07-10 Cristina Pignotti , Irene Reche Vallejo

We study a Cucker-Smale-type flocking model with distributed time delay where individuals interact with each other through normalized communication weights. Based on a Lyapunov functional approach, we provide sufficient conditions for the…

Analysis of PDEs · Mathematics 2019-07-16 Young-Pil Choi , Cristina Pignotti