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

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