Modelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package
Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, 14473, Potsdam, Germany
2 Institute of Physics and Astronomy, University of Potsdam, 14476, Potsdam, Germany
3 Department of Physics, Humboldt University of Berlin, 12489, Berlin, Germany
4 Institute for Theoretical Physics, University of Leipzig, 04103, Leipzig, Germany
5 Complexity Science, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, 14473, Potsdam, Germany
6 Department of Environmental Sciences, Copernicus Institute of Sustainable Development, Utrecht University, 3584 CB, Utrecht, The Netherlands
7 Stockholm Resilience Centre, Stockholm University, 10691, Stockholm, Sweden
Accepted: 21 April 2021
Published online: 11 June 2021
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.
© The Author(s) 2021
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