Related papers: The Vicsek-Kuramoto model in collective dynamics: …
Recently, Jadbabaie, Lin, and Morse (IEEE TAC, 48(6)2003:988-1001) offered a mathematical analysis of the discrete time model of groups of mobile autonomous agents raised by Vicsek et al. in 1995. In their paper, Jadbabaie et al. showed…
Noisy pursuit in complex environments drives emergent collective behaviors in active matter systems. A compelling platform to study the impact of environment cues is provided by the standard Vicsek model for studying flocking and swarming…
We propose a dynamic model for a system consisting of self-propelled agents in which the influence of an agent on another agent is weighted by geographical distance. A parameter $\alpha$ is introduced to adjust the influence: the smaller…
Information transfer is an essential factor in determining the robustness of collective behaviour in biological systems with distributed control. The most direct way to study the information transfer mechanisms is to experimentally detect…
We study a system of $N$ interacting particles moving on the unit sphere in $d$-dimensional space. The particles are self-propelled and coupled all to all, and their motion is heavily overdamped. For $d=2$, the system reduces to the classic…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and…
Human movement has been studied for decades and dynamic laws of motion that are common to all humans have been derived. Yet, every individual moves differently from everyone else (faster/slower, harder/smoother etc). We propose here an…
Self-propelled particles with alignment, displaying ordered collective motions such as swarming, can be investigated by the well-known Vicsek model. However, challenges still remain regarding the nature of the associated phase transition.…
Flocks of birds, schools of fish, insects swarms are examples of coordinated motion of a group that arises spontaneously from the action of many individuals. Here, we study flocking behavior from the viewpoint of multi-agent reinforcement…
The flocking of self-propelled particles in heterogeneous environments is relevant to both natural and artificial systems. The Vicsek model is a canonical choice to investigate such systems due to the minimal number of parameters required…
Collective motion is a fundamental phenomenon in biological swarms. As a framework for studying synchronization in motions, the Vicsek model is simple and efficient, assuming isotropic interactions with a complete field of view. Drawing…
We consider interacting particle dynamics with Vicsek type interactions, and their macroscopic PDE limit, in the non-mean-field regime; that is, we consider the case in which each particle/agent in the system interacts only with a…
We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally…
In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a…
Cyclic pursuit frameworks, which are built upon pursuit interactions between neighboring agents in a cycle graph, provide an efficient way to create useful global behaviors in a collective of autonomous robots. Previous work had considered…
In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body-attitude of an agent is modelled by a rotation matrix in $\mathbb{R}^3$ as in…
In biological systems, active agents such as actomyosin and cells move and interact on curved surfaces, exhibiting diverse phenomena. These observations have motivated studies of how curvature shapes their collective behavior. Here, using a…
Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
When particles move at a constant speed and have the tendency to align their directions of motion, ordered large scale movement can emerge despite significant levels of noise. Many variants of this model of self-propelled particles have…