Analytic description of adaptive network topologies in steady state

Abstract: In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in such active steady states. These distributions are shown to agree quantitatively with simulations except when rewiring is much faster than state update, and used to predict and to explain general properties of steady-state topologies. The method generalizes easily to other coevolutionary dynamics.