Reconstruction of nonlinear flows from noisy time series

Nonlinear dynamics is a rapidly developing subject across all disciplines involving spatial or temporal evolution. The reconstruction of equations motion for nonlinear system from observed time series has been hot topic long time. Nevertheless, in practice only partial information available many systems which are very likely contaminated with noise. Here, based on the invariance evolution equation an autonomous during translation, globally valid local approximation trajectory determined, could be reliably used vector fields unknown parameters functional forms, even observations. Moreover, noise interference nonlinearity computed to leading order, together global consideration bestows exceptional robustness and extra accuracy technique. new scheme asks solutions linear thus efficient, nicely demonstrated Lorenz different conditions, while FitzHugh–Nagumo (FHN) neural network model show its strength high dimensions.