Related papers: Synchronization on star graph with noise
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
We study synchronization properties of systems of Kuramoto oscillators. The problem can also be understood as a question about the properties of an energy landscape created by a graph. More formally, let $G=(V,E)$ be a connected graph and…
The Kuramoto model provides a concrete mathematical realization of emergent synchrony in a population of phase-coupled oscillators. Since Kuramoto's publication, \textit{Oscillations, Waves, and Turbulence}, researchers have worked to…
Phase turbulence is suppressed by applying common noise additively to the Kuramoto-Sivashinsky type equation, and the noise-induced phase synchronization is realized. The noise strength necessary for the suppression of phase turbulence is…
We study synchronization processes in networks of slightly non identical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in…
Knowledge graphs serve as critical resources supporting intelligent systems, but they can be noisy due to imperfect automatic generation processes. Existing approaches to noise detection often rely on external facts, logical rule…
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…
The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and…
A graph $\mathcal{G}$ is referred to as $\mathsf{S}^1$-synchronizing if, roughly speaking, the Kuramoto-like model whose interaction topology is given by $\mathcal{G}$ synchronizes almost globally. The Kuramoto model evolves on the unit…
The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…
The Kuramoto model is a commonly used mathematical model for studying synchronized oscillations in biological systems, with its temporal synchronization properties well studied. However, the properties of spatial waves have received less…
In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average…
Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal…
We discuss in detail a human scale example of the synchronization phenomenon, namely the dynamics of the rhythmic applause. After a detailed experimental investigation, we describe the phenomenon with an approach based on the classical…
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…
We study the synchronized behavior of the inertial Kuramoto oscillators with frustration effect under a symmetric and connected network. Due to the lack of second-order gradient flow structure and singularity of second-order derivative of…
We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to…
The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical…
Dynamics of complex systems are often driven by interactions that extend beyond pairwise links, underscoring the need to establish a correspondence between interpretable system parameters and emergent phenomena in hypergraph-based networks.…
In this article we study synchronization of Kuramoto oscillators with heterogeneous frequencies, and where underlying topology is a graph of diameter two. When the coupling strengths between every two connected oscillators are the same, we…