Foundations of Adaptive Networks (Adaptive Temporal Network Models)

Consider a disease spreading through a population. The network of physical contacts among humans plays a crucial role in governing such a dynamic contagion process. However, the social contact network itself is not a static entity – rather, it is influenced by the disease that is spreading across it (e.g., by impairing mobility through lockdowns, or by individuals taking precautionary measures and cutting down on social contact). Such a two-way feedback between the dynamics on the network and dynamics of the network is not unique to the spread of diseases, and is arguably at play in many of the most complex and consequential real-world networks, such as those underlying numerous infrastructural, ecological, and social systems. Adaptive networks – a class of models describing the dynamic dependencies between node-variables and network structure [1] – provide an excellent framework to probe such interdependencies in complex systems. 

In adaptive networks, timescales play a crucial role: processes at the level of nodes, for instance, may occur on a much faster timescale than changes in network connectivity, or vice versa, in which case mathematical idealizations are applicable (timescale separation). In contrast, in many real-world systems, the node-level and network-level processes occur on comparable timescales, preventing the aforementioned mathematical simplifications, and in some cases leading to complex dynamical interplays between structure and function, such as sociopolitical fragmentation [2] and self-organized criticality [3, 4]. Furthermore, as the name suggests, adaptation is a crucial aspect of these systems – namely, the network structure adaptively responds to the process running atop the network, and meanwhile, the node-variables adaptively respond to changes of the network. Consequently, this work isclosely related to the Santa Fe Institute’s research theme Complex Time – Adaptation, Aging, and the Arrow of Time. Namely, the core Complex Time concepts of complexity, temporality, and adaptation are manifest attributes of adaptive network models. 

rev. 5/4/2021 

While present-day adaptive network models have been developed to describe numerous real-world complex networks, the present literature’s account of adaptive networks remains fragmented. In this proposed working group (WG), we seek to bring together experts working on different aspects of adaptive network models and work towards clarifying and advancing the theoretical foundations of such models. A particular emphasis will be on the insights obtainable by taxonomizing the dependency structure and investigating implied intermediate-complexity models to establish a bridge for analytical progress in full-fledged adaptive network models and their applications to real-world complex systems. 

This event is supported by the James S. McDonnell Foundation Grant Number 220020491, Adaptation, Aging, and the Arrow of Time. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the James S. McDonnell Foundation.