An independent test of methods of detecting system states and bifurcations in time-series data

We present an independent test of recently developed methods of potential analysis and degenerate fingerprinting which aim, respectively, to identify the number of states in a system, and to forecast bifurcations. Several samples of modelled data of unknown origin were provided by one author, and the methods were used by the two other authors to investigate these properties. The main idea of the test was to investigate whether the techniques are capable to identify the character of the data of unknown origin, which includes potentiality, possible transitions and bifurcations. Based on the results of the analysis, models were proposed that simulated data equivalent to the test samples. The results obtained were compared with the initial simulations for critical evaluation of the performance of the methods. In most cases, the methods successfully detected the number of states in a system, and the occurrence of transitions between states. The derived models were able to reproduce the test data accurately. However, noise-induced abrupt transitions between existing states cannot be forecast due to the lack of any change in the underlying potential.