Related papers: Synchronization on circles and spheres with nonlin…
The Kuramoto model is a classical nonlinear ODE system designed to study synchronization phenomena. Each equation represents the phase of an oscillator and the coupling between them is determined by a graph. There is an increasing interest…
We construct a system of $N$ interacting particles on the unit sphere $S^{d-1}$ in $d$-dimensional space, which has $d$-body interactions only. The equations have a gradient formulation derived from a rotationally-invariant potential of a…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…
The goal of the present paper is to highlight the fundamental differences of so-called synchronization or consensus algorithms when the agents to synchronize evolve on a compact homogeneous manifold (like the circle, sphere or the group of…
We study the nonconvex optimization landscapes of synchronization problems on spheres. First, we present new results for the statistical problem of synchronization over the two-element group $\mathbf{Z}_2$. We consider the nonconvex…
This paper considers the synchronization problem for networks of coupled nonlinear dynamical systems under switching communication topologies. Two types of nonlinear agent dynamics are considered. The first one is non-expansive dynamics…
This paper considers a mean-field model of $n$ interacting particles whose state space is the unit circle, a generalization of the classical Kuramoto model. Global synchronization is said to occur if after starting from almost any initial…
Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the…
We present a model of synchronization in networks of autonomous agents where the topology changes due to agents motion. We introduce two time scales, one for the topological change and another one for local synchronization. If the former…
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been…
Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…
We investigate macroscopic behavior of a dynamical network consisting of a time-evolving wiring of interactions among a group of random walkers. We assume that each walker (agent) has an oscillator and show that depending upon the nature of…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…
Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines,…
Synchronization of coupled oscillators is a fundamental process in both natural and artificial networks. While much work has investigated the asymptotic stability of the synchronous solution, the fundamental question of the transient…
The structure of many real-world systems is best captured by networks consisting of several interaction layers. Understanding how a multi-layered structure of connections affects the synchronization properties of dynamical systems evolving…
We analyze two classes of Kuramoto models on spheres that have been introduced in previous studies. Our analysis is restricted to ensembles of identical oscillators with the global coupling. In such a setup, with an additional assumption…
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…