Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems

Abstract

Reconstruction of nonlinear dynamical systems from noisy time series data has attracted much attention in recent years, and it has broad applications in many fields, especially in theoretical biology. Here, we propose a reconstruction algorithm based on the noise-tolerant algebraic approach that can infer underlying continuous-time polynomial dynamical systems from the observed time series data. The advantages of our approach are that it can handle nonlinearity, and it can be applied to noisy systems. Our approach reduces the range of monomials to be considered without any a priori knowledge as many other studies does. We apply the proposed method to two oscillatory systems (the FitzHugh–Nagumo and the Oregonator) subject to noise, where the conventional fitting methods based on $$L_{1}$$ and $$L_{2}$$ regularizations often fail. Our numerical experiments show that the proposed method accurately reconstructs the continuous-time polynomial dynamical systems. We also apply the method to a chaotic system and show the effectiveness of our approach.