Mean-field theory for double-well systems on degree-heterogeneous networks
Mean-field theory for double-well systems on degree-heterogeneous networks
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DOI：
10.1098/rspa.2022.0350
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发表时间：
2022-08-31
影响因子：
3.5
通讯作者：
Masuda, Naoki
中科院分区：
文献类型：
--
作者：
Kundu, Prosenjit;MacLaren, Neil G.;Masuda, Naoki
在真实的世界中，许多复杂的动力系统，包括生态、气候、金融和电网系统，经常会出现临界转变或临界点，在临界点系统的动力学突然转变成一个性质不同的状态。在数学模型中，临界点发生在控制参数逐渐变化并超过一定阈值时。这种系统中的倾卸元件可以作为网络彼此相互作用，并且由于源自网络的高维数，理解相互作用的倾卸元件的行为是一个挑战。在这里，我们开发了一个基于度的平均场理论的一个典型的双阱系统耦合在一个网络上的目的是理解耦合倾翻动力学与低维描述。该方法近似的临界点和平衡的位置与一个合理的精度的发病。基于发展的理论和数值模拟，我们还提供了证据的多级临界点转变的网络中的双阱系统。
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.