State- and Distance-Dependent Adaptive Rewiring in Spatial Networks

Many systems can be modeled as a collection of dynamical units coupled via a network. In adaptive systems, network connectivity and dynamics are interdependent. For example, in neuroanatomical systems, the coupling between neural units influences their dynamical patterns, which can in turn reshape network structure via processes such as activity-dependent rewiring. However, another important aspect of many real-world networks is that they are embedded into space and may be subject to tradeoffs between material costs and efficiency. To take into account this feature, here we consider adaptive, but spatially-embedded networks of Kuramoto oscillators. Beginning with a random topology, we simulate a coevolution process that depends on both the dynamical states of coupled units, as well as spatial distances between them. In particular, edges tend to break between less dynamically coherent units, and are reformed based on proximity, such that short distance connections are favored. We examine the resulting dynamics of the system and the structural properties of the evolving network. We find that the interplay between dynamics, connectivity, and spatial constraints can generate interesting organizational features, such as spatially-localized modules.