Noise Bridges Dynamical Correlation and Topology in Coupled Oscillator Networks

Abstract

We study the relationship between dynamical properties and interaction patterns in complex oscillator networks in the presence of noise. A striking finding is that noise leads to a general, one-to-one correspondence between the dynamical correlation and the connections among oscillators for a variety of node dynamics and network structures. The universal finding enables an accurate prediction of the full network topology based solely on measuring the dynamical correlation. The power of the method for network inference is demonstrated by the high success rate in identifying links for distinct dynamics on both model and real-life networks. The method can have potential applications in various fields due to its generality, high accuracy, and efficiency.

Network Dynamics as an Inverse Problem

“…And, although successful, most of these approaches start to fail when the size of the network and the number of incoming connections per node increases. Therefore, their applicability is reduced to relatively small networks (except for [112]). The second, inference from model fitting [34,35,69], recovers connections by fitting pre-imposed models for nodal dynamics to recorded time series.…”

“…The first, inference from statistical similarity measures [105,112,113], recovers links among oscillators from statistical dependency measures applied on units' time series. And, although successful, most of these approaches start to fail when the size of the network and the number of incoming connections per node increases.…”

Synchronization of Time-Delay Chaotic System in Presence of Noise

“…And the effect of the noise on dynamical systems has been a fundamental issue in nonlinear and statistical physics [13][14][15][16][17] . It has been found that noise, under some conditions, can induce or enhance synchronization even in the absence of coupling [15][16][17] .…”

Network Reconstruction Based on Evolutionary-Game Data via Compressive Sensing

“…Examples of potential applications abound: reconstruction of gene-regulatory networks based on expression data in systems biology [1][2][3][4], extraction of various functional networks in the human brain from activation data in neuroscience [5][6][7][8], and uncovering organizational networks based on discrete data or information in social science and homeland defense. In the past few years, the problem of network reconstruction has received growing attention [9][10][11][12][13][14][15][16]. Most existing works were based, however, on networks of oscillators whose dynamics are mathematically described by coupled, continuous differential equations.…”

“…Most existing works were based, however, on networks of oscillators whose dynamics are mathematically described by coupled, continuous differential equations. In particular, either some knowledge about the dynamical evolution of the underlying networked system is needed [9][10][11] or long, oscillatory signals in continuous time are required [12][13][14][15][16]. The advantage of availing oneself of continuous-time data is lost for networks in social, economic, and even biological sciences where node-to-node interactions are governed by evolutionary-game types of dynamics [17][18][19][20][21].…”