Mean-field theory for double-well systems on degree-heterogeneous networks

Prosenjit Kundu, Neil G. Maclaren, Hiroshi Kori, Naoki Masuda*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Many complex dynamical systems in the real world, including ecological, climate, financial and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and crosses a certain threshold. Tipping elements in such systems may interact with each other as a network, and understanding the behaviour of interacting tipping elements is a challenge because of the high dimensionality originating from the network. Here, we develop a degree-based mean-field theory for a prototypical double-well system coupled on a network with the aim of understanding coupled tipping dynamics with a low-dimensional description. The method approximates both the onset of the tipping point and the position of equilibria with a reasonable accuracy. Based on the developed theory and numerical simulations, we also provide evidence for multistage tipping point transitions in networks of double-well systems.

Original languageEnglish
Article number20220350
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2264
Publication statusPublished - 2022 Aug 31
Externally publishedYes


  • critical transition
  • degree-based mean-field theory
  • networks
  • tipping point

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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