Related papers: Clusters in nonsmooth oscillator networks
We explore oscillatory behaviour in a family of periodically driven spin chains which are subject to a weak measurement followed by post-selection. We discover a transition to an oscillatory phase as the strength of the measurement is…
Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention…
Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological…
In this paper the collective dynamics of $N$-coupled piecewise linear (PWL) systems with different number of scrolls and coupled in a master-slave sequence configuration is studied, i.e. a ring connection with unidirectional links.…
We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. The methods commonly used to study cluster synchronization in networks of coupled oscillators ground on simplifying…
This paper presents a master stability function (MSF) approach for analyzing the stability of amplitude death (AD) in networks of delay-coupled oscillators. Unlike the familiar MSFs for instantaneously coupled networks, which typically have…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
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…
We investigate the collective dynamics of chaotic multi-stable Duffing oscillators connected in different network topologies, ranging from star and ring networks, to scale-free networks. We estimate the resilience of such networks by…
Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this…
Designing stable cluster synchronization patterns is a fundamental challenge in nonlinear dynamics of networks with great relevance to understanding neuronal and brain dynamics. So far, cluster synchronization has been studied exclusively…
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the…
The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…
Identifying key players in a set of coupled individual systems is a fundamental problem in network theory. Its origin can be traced back to social sciences and led to ranking algorithms based on graph theoretic centralities. Coupled…
Understanding the global dynamical behaviour of a network of coupled oscillators has been a topic of immense research in many fields of science and engineering. Various factors govern the resulting dynamical behaviour of such networks,…
The problem of finding clusters in complex networks has been extensively studied by mathematicians, computer scientists and, more recently, by physicists. Many of the existing algorithms partition a network into clear clusters, without…
Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function (WSF), might vary from cycle to cycle. When there are finite different WSFs, $s_1,\ldots,s_K$,…
Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a…