Predicting critical transitions induced by the saddle-node bifurcation in electronic circuits using parameter space estimation.

Abstract

This study predicts critical transitions induced by the saddle-node bifurcation in electronic circuits only from time-series datasets through parameter space estimation. By estimating the parameter space, we plot a bifurcation diagram and approximate Lyapunov exponents of an unknown system, enabling the accurate prediction of critical transitions. The parameter space estimation identifies the target system from time-series data measured before the critical transitions, incorporating shifts in system dynamics due to parameter changes. Assuming continuous and gradual parameter changes, it estimates the subsequent shifts and predicts when the critical transitions occur. Previous studies have utilized parameter space estimation to predict the critical transitions, as these transitions are bifurcation phenomena resulting from changes in system parameters. The parameter space estimation utilizes the universal characteristic of the Lyapunov exponents approaching zero at the critical transitions, which is independent of specific systems, allowing for generalized predictions. This research employs electronic circuits configured to represent two types of biomass models, where critical transitions occur. Time-series data measured from the electronic circuits are used as target datasets. One biomass model is a one-dimensional model commonly used for critical transition detection, while the other is a two-dimensional model exhibiting seasonality. The time-series datasets are influenced by dynamical noise and contaminated by observational noise. We demonstrate that system dynamics, attracted to equilibrium, can be extracted from the datasets using parameter space estimation with an extreme learning machine, which possesses strong generalization properties. Furthermore, to assess the proximity to the critical transition after the training phase for parameter space estimation, this study demonstrates the feasibility of predicting changes in parameter values within the estimated parameter space. Predicting the parameter values is crucial for continuous system monitoring and updating predictions as new information emerges, thereby ensuring timely and precise responses to potential critical transitions.