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Stability breakdown along a line of equilibria in nonlinear circuits with memristors

The design in 2008 of a device with a memristive 
characteristic has had a great impact in electronics, specially at the nanometer scale. This device, whose existence was predicted by Leon Chua in 1971 for symmetry reasons, is governed in a flux-controlled setting by a relation of the form i = W(ϕ)v, and systematically leads 
to the presence of non-isolated equilibria. In this communication we examine how the stability of such manifolds of equilibria may break down when normal hyperbolicity fails. This phenomenon may be due 
to the transition of an eigenvalue either through the origin or through infinity. Our approach is a graph-theoretic one, aiming at the analysis of such phenomena in terms of the topology of the digraph underlying the circuit.