Abstract
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 of 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 (https://doi.org/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.
Highlights
Sustainable future lies well within the scope of desired tipping events [13]
We describe the general structure of our package (Sect. 2.2), the building blocks of nonlinear dynamical systems, namely the tipping elements and their interaction structure (Sect. 2.3) as well as the network types natively included in the package (Sect. 2.4) and lastly, the extension to several types of stochastic tipping elements (Sect. 2.5)
For 2 ◦C, we find that the likelihood of tipping is around 50% for the Greenland Ice Sheet (GIS) and West Antarctic Ice Sheet (WAIS), while it is significantly lower for the Atlantic Meridional Overturning Circulation (AMOC) and the Amazon Rainforest (AR)
Summary
Building upon recent developments in studying interacting nonlinear dynamics on complex networks [30,31,32,33,34], we here introduce the unified Python package PyCascades. 2.2), the building blocks of nonlinear dynamical systems, namely the tipping elements and their interaction structure 2.3) as well as the network types natively included in the package 2.4) and lastly, the extension to several types of stochastic tipping elements We use our model to simulate tipping cascades in the Amazon rainforest, which is connected by a network of atmospheric moisture flows We exchange the fundamental differential equation that has been used in the two earlier examples to model tipping cascades in an economic example of a global trade network
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