Nonlinear dynamics of memristor oscillators via the flux-charge analysis method

A recent work [1] introduced a flux-charge analysis method (FCAM) to study the nonlinear dynamics and bifurcations of a large class of memristor circuits. FCAM relies on the use of Kirchhoff Flux and Charge Laws and constitutive relations of circuits elements in the flux-charge domain. In [1], the saddle-node bifurcations of equilibrium points in the simplest memristor circuit composed of an ideal flux-controlled memristor and a capacitor, were studied. This paper is devoted to analyze via FCAM more complex bifurcations, such as Hopf bifurcations and period-doubling bifurcations originating complex attractors, in higher-order memristor circuits. It is shown analytically and quantitatively how these bifurcations can be induced by varying the initial conditions of dynamic circuit elements in the voltage-current domain while assuming that circuits parameters are held fixed. Such bifurcations are known in the literature as bifurcations without parameters.