Reconstructing nonlinear networks subject to fast-varying noises by using linearization with expanded variables

Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly affect. In this Letter, we propose a general method that introduc...

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Bibliographic Details
Published in:arXiv.org 2017-10
Main Authors: Shi, Rundong, Hu, Gang, Wang, Shihong
Format: Article
Language:English
Subjects:
Dynamical systems
Linearization
Networks
Noise
Noise measurement
Nonlinear differential equations
Nonlinear dynamics
Nonlinear equations
Nonlinearity
System dynamics
Online Access:Get full text
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Summary:Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly affect. In this Letter, we propose a general method that introduces a number of nonlinear terms of the measurable variables as artificial and new variables, and uses the expanded variables to linearize nonlinear differential equations. Moreover, we use two-time correlations to decompose effects of system dynamics and noise driving. With these transformations, reconstructing nonlinear dynamics of the original system is equivalent to solving linear dynamics of the expanded system at the least squares approximations. We can well reconstruct nonlinear networks, including all dynamic nonlinearities, network links, and noise statistical characteristics, as sampling frequency is rather low. Numerical results fully verify the validity of theoretical derivations.
ISSN:2331-8422