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

Research output: Contribution to journalArticle

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Abstract

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
Volume91
Issue number5
DOIs
Publication statusPublished - 7 May 2015

Keywords

  • water temple networks
  • statistical-mechanics
  • system
  • model
  • game

Cite this

Macroscopic description of complex adaptive networks co-evolving with dynamic node states. / Wiedermann, Marc (Corresponding Author); Donges, Jonathan F; Heitzig, Jobst; Lucht, Wolfgang; Kurths, Jurgen.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 91, No. 5, 052801, 07.05.2015.

Research output: Contribution to journalArticle

Wiedermann, Marc ; Donges, Jonathan F ; Heitzig, Jobst ; Lucht, Wolfgang ; Kurths, Jurgen. / Macroscopic description of complex adaptive networks co-evolving with dynamic node states. In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics. 2015 ; Vol. 91, No. 5.
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abstract = "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.",
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