Synchronization in Electrical Circuits With Memristors and Grounded Capacitors

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.