Predicting the parameter value at which a critical transition occurs from the Lyapunov exponents in an estimated parameter space

Abstract

This study estimates a parameter space from only two time-series data sets in order to predict when a critical transition occurs caused by a saddle-node bifurcation. By estimating the parameter space, we can plot a bifurcation diagram corresponding to the original bifurcation diagram. In addition, the Lyapunov exponent can also be approximated in the estimated parameter space and corresponds to the bifurcation diagram. Thereby, we expect that the parameter value at which the critical transition occurs is predicted. In numerical experiments, we estimate the parameter space for the coupled dynamics of water and vegetation, and we compare the bifurcation diagrams in the original and estimated parameter spaces. For predicting when the critical transition occurs, we confirm that the Lyapunov exponent reaches zero when the critical transition occurs. In addition, we compare the prediction results between the proposed method and early warning signals.