Detecting and Predicting Tipping Points

Xiaoyi Peng, Michael Small, Yi Zhao, Jack Murdoch Moore

Research output: Contribution to journalArticle

1 Citation (Scopus)


Tipping points are sudden, and sometimes irreversible and catastrophic, changes in a system's dynamical regime. Complex networks are now widely used in the analysis of time series from a complex system. In this paper, we investigate the scope of network methods to indicate tipping points. In particular, we verify that the permutation entropy of transition networks constructed from time series observations of the logistic map can distinguish periodic and chaotic regimes and indicate bifurcations. The permutation entropy of transition networks, the mean edge between-ness of visibility graphs and the number of code words in compression networks, are each shown to indicate the onset of transition of a pitchfork bifurcation system. Our study shows that network methods are effective in detecting transitions. Network-based forecasts can be applied to models of real systems, as we illustrate by considering a lake eutrophication model.

Original languageEnglish
Article number1930022
Number of pages11
JournalInternational Journal of Bifurcation and Chaos
Issue number8
Publication statusPublished - Jul 2019

Cite this