Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 478, Issue 2264, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2022.0350
Keywords
tipping point; critical transition; networks; degree-based mean-field theory
Categories
Funding
- JSPS KAKENHI [21K12056]
- AFOSR European Office [FA9550-19-1-7024]
- Sumitomo Foundation
- Japan Science and Technology Agency (JST) [JPMJMS2021]
- National Science Foundation [2052720]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [2052720] Funding Source: National Science Foundation
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In this paper, a degree-based mean-field theory is developed for understanding the coupled tipping dynamics in a network of double-well systems. The study provides evidence for multistage tipping point transitions in such networks.
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.
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