In this paper, we consider the terminal behaviour of resistive electrical networks that are subject to changes or re-design. Specifically, we study the robustness of the effective resistance as a measure of this terminal behaviour. We give an explicit expression of how the effective resistance changes as a result of network perturbations, e.g., the addition/deletion of edges or changes in the conductance value. This expression has a clear interpretation and allows for efficient numerical evaluation. We extend this result to the total effective resistance, which can be regarded as a performance measure of consensus networks. In addition, these results are used to derive a graphtheoretical characterisation of the effective resistance.
Motivated by neuromorphic computing applications, this letter considers electrical circuits comprising memristors and grounded capacitors, connected to external sources. By using the flux-charge domain modelling approach, we will derive an initial value problem describing the dynamic behaviour of this circuit. Given an initial value and a fixed input, we will show that the fluxes in this circuit converge to an equilibrium. Furthermore, we show that when the fluxes reach this equilibrium, we achieve voltage synchronisation, i.e., no more currents are flowing through the circuit. These results are emphasised in an illustration.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.