Abstract
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.
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