Slow relaxation of disordered memristive networks

Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. Using graph-theoretic tools, we show that the memory dynamics promotes scale-free relaxation even for the simplest model of linear memristors. In this case, we are also able to describe the memory evolution in terms of orthogonal projection operators onto the subspace of fundamental current loops. This orthogonal projection explicitly reveals the coupling between the spatial and temporal sectors of the dynamics and the emergence of a power law relaxation as a superposition of exponential relaxation times with a broad range of scales. This glassy behavior suggests a much richer dynamics of memristive networks than previously considered.