It is a fundamental challenge to understand how the function of a network is related to its
structural organization. Adaptive dynamical networks represent a broad class of systems that …

Moment closure methods appear in myriad scientific disciplines in the modelling of complex
systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled …

Traditionally, much of the study of networks has focused on structural features. Indeed,
mathematical subjects such as graph theory have a rich history of investigating network …

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and
technology. For example, adaptive couplings appear in various real-world systems, such as …

Collective decision making processes lie at the heart of many social, political, and economic
challenges. The classical voter model is a well-established conceptual model to study such …

Today, humans have a critical impact on the Earth system and vice versa, which can
generate complex feedback processes between social and ecological dynamics. Integrating …

In this Letter, a generalization of pairwise models to non-Markovian epidemics on networks
is presented. For the case of infectious periods of fixed length, the resulting pairwise model …

Dispersal and foodweb dynamics have long been studied in separate models. However,
over the past decades, it has become abundantly clear that there are intricate interactions …

The study of motifs can help researchers uncover links between the structure and function of
networks in biology, sociology, economics, and many other areas. Empirical studies of …

We present a full stochastic description of the pair approximation scheme to study binary-
state dynamics on heterogeneous networks. Within this general approach, we obtain a set of …