Continuum limits for adaptive network dynamics

Adaptive (or co-evolutionary) network dynamics, i.e., when changes of the network/graph topology are coupled with in node/vertex can give rise to rich and complex dynamical behavior. Even though adaptivity improve modelling collective phenomena, it often complicates analysis corresponding mathematical models significantly. For non-adaptive systems, a possible way tackle this problem is by passing so-called continuum or mean-field limits, which describe system limit infinitely many nodes. Although fully adaptive dynamic have been used lot recent years applications, we still lacking detailed theory for large-scale limits. example, limits static temporal networks already established literature certain models, yet has open so far. In paper introduce rigorously justify sequences Kuramoto-type models. The resulting integro-differential equations allow us incorporate large class co-evolving graphs high density. Furthermore, use very general measure-theoretical framework our proof representing (infinite) graph thereby also providing structural basis even larger classes As an application theory, consider Kuramoto model directly motivated from neuroscience studied Berner et al.~in using numerical techniques formal stability analysis.