Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives
This paper presents a review and critical analysis on the modeling of the dynamics of
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …
Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
Many biological and neural systems can be seen as networks of interacting periodic
processes. Importantly, their functionality, ie, whether these networks can perform their …
processes. Importantly, their functionality, ie, whether these networks can perform their …
A mathematical perspective on transformers
B Geshkovski, C Letrouit, Y Polyanskiy… - ar** in the Kuramoto model
We consider the Kuramoto model of globally coupled phase oscillators in its continuum limit,
with individual frequencies drawn from a distribution with density of class C^ n C n (n ≧ 4 …
with individual frequencies drawn from a distribution with density of class C^ n C n (n ≧ 4 …
Multi-population phase oscillator networks with higher-order interactions
The classical Kuramoto model consists of finitely many pairwisely coupled oscillators on the
circle. In many applications a simple pairwise coupling is not sufficient to describe real-world …
circle. In many applications a simple pairwise coupling is not sufficient to describe real-world …
Particle and kinetic models for swarming particles on a sphere and stability properties
We present particle and kinetic models for the description of swarming particles on a sphere
in the presence of random noises, and study their stability properties. In the absence of …
in the presence of random noises, and study their stability properties. In the absence of …