Macroscopic description of complex adaptive networks co-evolving with dynamic node states

Marc Wiedermann* (Corresponding Author), Jonathan F Donges, Jobst Heitzig, Wolfgang Lucht, Jurgen Kurths

*Corresponding author for this work

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In many real-world complex systems, the time evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here we study opinion formation and imitation on an adaptive complex network which is dependent on the individual dynamic state of each node and vice versa to model the coevolution of renewable resources with the dynamics of harvesting agents on a social network. The adaptive voter model is coupled to a set of identical logistic growth models and we mainly find that, in such systems, the rate of interactions between nodes as well as the adaptive rewiring probability are crucial parameters for controlling the sustainability of the system's equilibrium state. We derive a macroscopic description of the system in terms of ordinary differential equations which provides a general framework to model and quantify the influence of single node dynamics on the macroscopic state of the network. The thus obtained framework is applicable to many fields of study, such as epidemic spreading, opinion formation, or socioecological modeling.
Original languageEnglish
Article number052801
Number of pages11
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number5
Publication statusPublished - 7 May 2015

Bibliographical note

This work was carried out within the framework of PIK’s COPAN project. M.W. was supported by the German Federal Ministry for Science and Education via the BMBF Young Investigators Group CoSy-CC2 (Grant No. 01LN1306A). J.F.D. and W.L. acknowledge funding from the Stordalen Foundation (Norway) via the initiative and BMBF (project GLUES) and J.K. acknowledges the IRTG 1740 funded by Deutsche Forschungsgesellschaft (DFG) (Germany) and FAPESP. We thank R. V. Donner for helpful comments and suggestions on the manuscript and R. Grzondziel and C. Linstead for help with the IBM iDataPlex Cluster at the
Potsdam Institute for Climate Impact Research.


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