Dynamic Analysis of Memristor Circuits via Input–Output Techniques

The chapter reviews a recently proposed input–output approach to investigate the dynamics of a class of circuits composed of a linear time-invariant two-terminal element coupled with one ideal flux-controlled memristor. The classical (autonomous) Chua’s and (non-autonomous) Murali–Lakshmanan–Chua’s memristor circuits are employed to discuss the features of the approach, which can be seen as the input–output counterpart of the Flux–Charge Analysis Method (FCAM). It is shown that the dynamics of any circuit of the class admits a first integral, which implies that the circuit dynamics can be obtained by collecting those displayed by a canonical reduced-order input–output system subject to a constant input with a varying amplitude. More specifically, there is a one to one correspondence between the dynamics of the canonical input–output system generated by a fixed amplitude of the constant input and the dynamics displayed by the memristor circuit onto one of the infinite invariant manifolds. It is also shown that the canonical input–output representation of both Chua’s and Murali–Lakshmanan–Chua’s memristor circuits can be implemented via a circuit with a voltage-controlled nonlinear resistor in place of the memristor plus an additional constant voltage source, thus establishing an interesting similarity between memristor circuits and memristor-less circuits. The memristor-less versions are then employed to investigate some features of the dynamics of both Chua’s and Murali–Lakshmanan–Chua’s memristor circuits.