## 抄録

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.

本文言語 | English |
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論文番号 | 20220350 |

ジャーナル | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

巻 | 478 |

号 | 2264 |

DOI | |

出版ステータス | Published - 2022 8月 31 |

## ASJC Scopus subject areas

- 数学 (全般)
- 工学（全般）
- 物理学および天文学（全般）