Related papers: Synchronization and modularity in complex networks
The extension of the master stability function (MSF) to analyze stability of generalized synchronization for coupled nearly identical oscillators is discussed. The nearly identical nature of the coupled oscillators comes from some parameter…
Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The method of averaging plays an important role in stability analysis, but the standard Lyapunov's second method is not applicable due to the lack of…
In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a…
Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the…
The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each characterized by a scalar phase and a natural frequency, by…
Complex networks often have a modular structure, where a number of tightly- connected groups of nodes (modules) have relatively few interconnections. Modularity had been shown to have an important effect on the evolution and stability of…
In this paper we study synchronized motions in complex networks in which there are distinct groups of nodes where the dynamical systems on each node within a group are the same but are different for nodes in different groups. Both…
This paper studies stability properties of multi-cluster formations in Kuramoto networks with adaptive coupling. Sufficient conditions for the local asymptotic stability of the corresponding synchronization invariant toroidal manifold are…
The stability analysis of synchronization in time-varying higher-order networked structures (simplicial complexes) is one of the challenging problem due to the presence of time-varying group interactions. In this context, most of the…
The problem of synchronization in networks of neural mass model populations with discrete couplings is considered. The considered network is hybrid one, therefore Mikheev approach is applied to transform it to the network with time-varying…
A small-world network (SW) of similar phase oscillators, interacting according to the Kuramoto model is studied numerically. It is shown that deterministic Kuramoto dynamics on the SW networks has various stable stationary states. This can…
Despite growing interest in synchronization dynamics over "higher-order" network models, optimization theory for such systems is limited. Here, we study a family of Kuramoto models inspired by algebraic topology in which oscillators are…
The Kuramoto model has shaped our understanding of synchronization in complex systems, yet its phase-only formulation neglects amplitude dynamics that are intrinsic to many oscillatory networks. In this work, we revisit Kuramoto-type…
We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital…
Synchronization is a widespread phenomenon observed across natural and artificial networked systems. It often manifests itself by clusters of units exhibiting coincident dynamics. These clusters are a direct consequence of the organization…
The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized…
We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than…
Future communication networks are expected to feature autonomic (or self-organizing) mechanisms to ease deployment (self-configuration), tune parameters automatically (self-optimization) and repair the network (self-healing).…
Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order…
It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast…