复杂网络上相互作用临界元素的非线性动力学建模：PyCascades 软件包
Modelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package
AI总结：
本文介绍了开源 Python 软件包 PyCascades，用于建模复杂网络上相互作用的临界元素的非线性动力学，以研究潜在危险的级联效应，并展示了其在亚马逊雨林水分循环网络、地球系统临界元素和全球贸易网络中的三种应用。
摘要：
临界元素出现在诸如社会经济、生态和气候系统等各种系统中。在许多情况下，单个临界元素并非相互独立，而是在时间和空间上跨尺度相互作用。为了对相互作用的临界元素系统进行建模，我们在此介绍用于研究相互作用临界元素的开源软件包 PyCascades（doi: 10.5281/zenodo.4153102）。PyCascades 是一个用编程语言 Python 编写的面向对象且易于扩展的软件包。它允许研究在何种条件下，相互作用的动力系统之间可能会出现潜在危险的级联效应，重点关注临界元素。使用 PyCascades 可以使用不同类型的临界元素，例如 double-fold 和 Hopf 类型，以及它们之间的相互作用。PyCascades 可应用于任意的复杂网络结构，并且最近已扩展至随机动力系统。本文通过介绍其背后的基本概念和方法论，概述了 PyCascades 的功能。最后，讨论了三个示例，展示了该软件包的三种不同应用。首先，研究了亚马逊雨林的水分循环网络。其次，讨论了相互作用地球系统临界元素的模型。第三，将 PyCascades 建模框架应用于全球贸易网络。
英文摘要：
Tipping elements occur in various systems such as in socio-economics, ecology and the climate system. In many cases, the individual tipping elements are not independent from each other, but they interact across scales in time and space. To model systems of interacting tipping elements, we here introduce the PyCascades open source software package for studying interacting tipping elements (doi: 10.5281/zenodo.4153102). PyCascades is an object-oriented and easily extendable package written in the programming language Python. It allows for investigating under which conditions potentially dangerous cascades can emerge between interacting dynamical systems, with a focus on tipping elements. With PyCascades it is possible to use different types of tipping elements such as double-fold and Hopf types and interactions between them. PyCascades can be applied to arbitrary complex network structures and has recently been extended to stochastic dynamical systems. This paper provides an overview of the functionality of PyCascades by introducing the basic concepts and the methodology behind it. In the end, three examples are discussed, showing three different applications of the software package. First, the moisture recycling network of the Amazon rainforest is investigated. Second, a model of interacting Earth system tipping elements is discussed. And third, the PyCascades modelling framework is applied to a global trade network.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
