Related papers: Oscillations of simple networks
Natural and artificial networks, from the cerebral cortex to large-scale power grids, face the challenge of converting noisy inputs into robust signals. The input fluctuations often exhibit complex yet statistically reproducible…
We study the energy flow between a one dimensional oscillator and a chaotic system with two degrees of freedom in the weak coupling limit. The oscillator's observables are averaged over an initially microcanonical ensemble of trajectories…
We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…
As a quantification of the main bottleneck to flow over a graph, the network property of conductance plays an important role in the process of synchronization of network-coupled dynamical systems. Diffusive coupling terms serve not only to…
Causal inference provides an analytical framework to identify and quantify cause-and-effect relationships among a network of interacting agents. This paper offers a novel framework for analyzing cascading failures in power transmission…
We examine numerically the three-way relationships among structure, Laplacian spectra and frequency synchronization dynamics on complex networks. We study the effects of clustering, degree distribution and a particular type of coupling…
Series-parallel network topologies generally exhibit simplified dynamical behavior and avoid high combinatorial complexity. A comprehensive analysis of how flow complexity emerges with a graph's deviation from series-parallel topology is…
In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…
The eigenvalues of the normalized Laplacian of a graph provide information on its topological and structural characteristics and also on some relevant dynamical aspects, specifically in relation to random walks. In this paper we determine…
It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two…
Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined…
We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with…
The new proposed "energy gradient theory," which physically explains the phenomena of flow instability and turbulent transition in shear flows and has been shown to be valid for parallel flows, is extended to curved flows in this study.…
In this paper we derive an analytical expression for the mean load at each node of an arbitrary undirected graph for the uniform multicommodity flow problem under random walk routing. We show the mean load is linearly dependent on the nodal…
We consider transport in a fluid flow of arbitrary complexity but with a dominant flow direction. This is the situation encountered, for example, when analyzing the dynamics of sufficiently small particles immersed in a turbulent fluid and…
We study the effect of adding to a directed chain of interconnected systems a directed feedback from the last element in the chain to the first. The problem is closely related to the fundamental question of how a change in network topology…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
Online social networks suffer from explosive user dynamics such as flaming that can seriously affect social activities in the real world because the dynamics have growth rates that can overwhelm our rational decision making faculties.…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
Replacing conventional power sources by renewable sources in current power grids drastically alters their structure and functionality. The resulting grid will be far more decentralized with an distinctly different topology. Here we analyze…