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.

Sustainable use of renewable resources in a stylized social–ecological network model under heterogeneous resource distribution

“…We purposely do not model any form of individual learning of the agents with regard to the best harvesting strategy to emphasize the effects of the described social learning process. For homogeneous resource access (Wiedermann et al, 2015), one already observes a threshold in the parameter space of the model from non-sustainable to sustainable regimes at certain critical values φ c and τ c . Since the concrete heterogeneous resource distribution is often unknown, we show systematically how an increasing heterogeneity -starting from an almost homogeneous distribution -affects the critical transition parameters φ c and τ c .…”

Taxonomies for structuring models for World-Earth system analysis of the Anthropocene: subsystems, their interactions and social-ecological feedback loops

“…As in many models of the spread of social traits (e.g., Traulsen et al (2010); Wiedermann et al (2015)), we assume that each country i may adopt another country j's value of δ (social learning by imitation) and that the probability P for doing so depends on the difference between i and j's current utility, D ij (t) = U j (t)−U i (t), in a nonlinear, sigmoid-shaped fashion, with P (D) → 0 for D → −∞ and P (D) → 1 for D → ∞. The utility difference between a country using α and a country using β is 5 D(t) = [α − β](G − E 0 s(C(t)) + cs(C(t)) 2 φ(F (t)) − 1)…”

“…An example for CUL → ENV links are nature protection areas for biodiversity conservation in marine reserve mod- Policy measures such as taxes, regulations or caps are much studied by IAMs of anthropogenic climate change (Edenhofer et al, 2014), while influences of value and norm change on economic activities such as general resource use (Wiedermann et al, 2015;Barfuss et al, 2017) and fishing (Martin and Schlüter, 2015;Lade et al, 2015) has been studied in the social-ecological 10 modelling literature.…”

Towards representing human behavior and decision making in Earth system models – an overview of techniques and approaches

“…Other applications of coevolutionary network models allow us to understand the presence of social tipping points in opinion formation (Holme and Newman, 2006), epidemic spreading (Gross et al, 2006), the emergence of cooperation in social dilemmas (Perc and Szolnoki, 2010), and the interdependence of coalition formation with social networks (Auer et al, 2015). Such adaptive network models exhibit complex and nonlinear dynamics such as phase transitions (Holme and Newman, 2006), multi-stability (Wiedermann et al, 2015), oscillations in both agent states and network structure (Gross et al, 2006), and structural changes in network properties (Schleussner et al, 2016).…”

“…The agents interact on a social network, imitating the harvesting effort of neighbors that harvest more and may drop links to neighbors that use another effort. The interaction of the resource dynamics with the network dynamics either leads to a convergence of harvest efforts or a segregation of the community into groups with higher or lower effort depending on the model parameters (Wiedermann et al, 2015;Barfuss et al, 2017).…”