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

• Published in: Communications in nonlinear science & numerical simulation Vol. 72; pp. 407 - 416
• Main Authors: Shi, Rundong, Hu, Gang, Wang, Shihong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 30.06.2019; Elsevier Science Ltd
• Subjects: Approximation; Dynamical systems; Expanded variables; Least squares approximations; Linearization; Network reconstruction; Networks; Noise; Noise measurement; Nonlinear differential equations; Nonlinear dynamics; Nonlinear equations; Nonlinear systems; Nonlinearity; System dynamics; Time series; Nonlinear dynamics; Expanded variables; Least squares approximations; Noise; Network reconstruction
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2019.01.010

•Propose an approach to reconstruct noisy nonlinear networks from measure data.•Use the expanded variables to linearize nonlinear systems and solving nonlinear dynamics becomes solving linear dynamics at the least squares approximations.•Well infer nonlinear networks and noise statistics at low sampling frequencies. Reconstructing noisy 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 paper, 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 impacts. With these transformations, reconstructing nonlinear dynamics of original networks is approximately 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 justify the validity of theoretical derivations.