title: Macroscopic description of complex adaptive networks coevolving with dynamic node states.
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.
authors.affiliation: Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany, EU.|Department of Physics, Humboldt University, Newtonstr. 15, 12489 Berlin, Germany, EU.
authors.forename: Marc
authors.initials: M
authors.lastname: Wiedermann
authors.affiliation: Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany, EU.|Stockholm Resilience Centre, Stockholm University, Kräftriket 2B, 114 19 Stockholm, Sweden, EU.
authors.forename: Jonathan F
authors.initials: JF
authors.lastname: Donges
authors.affiliation: Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany, EU.
authors.forename: Jobst
authors.initials: J
authors.lastname: Heitzig
authors.affiliation: Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany, EU.|Department of Geography, Humboldt University, Rudower Chaussee 16, 12489 Berlin, Germany, EU.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Lucht
authors.affiliation: Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany, EU.|Department of Physics, Humboldt University, Newtonstr. 15, 12489 Berlin, Germany, EU.|Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX, United Kingdom, EU.|Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths
mesh_terms: D008962:Models, Theoretical; D060756:Social Networking; D013997:Time Factors