Harmonic balance method to analyze bifurcations in memristor oscillatory circuits

The paper studies nonlinear dynamics and bifurcations of a class of memristor oscillatory circuits obtained by replacing the nonlinear resistor of a Chua's oscillator with a flux-controlled memristor. A recently developed technique, named flux-charge analysis method, has shown that the state space of such circuits can be decomposed in invariant manifolds, where each manifold is characterized by a different dynamics and different attractors. Goal of the paper is to investigate the use of the harmonic balance method in combination with flux-charge analysis method in order to study the different kinds of bifurcations generated by changing the circuit parameters on a fixed manifold, changing manifold for a fixed parameter set (bifurcations without parameters), or changing simultaneously circuit parameters and manifolds. The main result is that the harmonic balance method is quite simple to apply in this rich bifurcation context and is effective to detect Hopf and to accurately predict period-doubling bifurcations of all these different kinds.