Memristor circuits: flux-charge analysis method

Memristor-based circuits are widely exploited to realize analog and/or digital systems for a broad scope of applications (e.g., amplifiers, filters, oscillators, logic gates, and memristor as synapses). A systematic methodology is necessary to understand complex nonlinear phenomena emerging in memristor circuits. The manuscript introduces a comprehensive analysis method of memristor circuits in the flux-charge (φ,q) -domain. The proposed method relies on Kirchhoff Flux and Charge Laws and constitutive relations of circuit elements in terms of incremental flux and charge. The main advantages (over the approaches in the voltage-current (v,i) -domain) of the formulation of circuit equations in the (φ,q) -domain are: a) a simplified analysis of nonlinear dynamics and bifurcations by means of a smaller set of ODEs; b) a clear understanding of the influence of initial conditions. The straightforward application of the proposed method provides a full portrait of the nonlinear dynamics of the simplest memristor circuit made of one memristor connected to a capacitor. In addition, the concept of invariant manifolds permits to clarify how initial conditions give rise to bifurcations without parameters.