Memristor models for pattern recognition systems

The design of Memristor Oscillatory Neurocomputers for pattern recognition tasks may not leave aside a preliminary thorough investigation of the nonlinear dynamics of the whole system and its basic components. This chapter yields novel insights into the peculiar nonlinear dynamics of different memristor models. A detailed mathematical treatment aimed at highlighting the key impact the initial condition on the flux across a memristor with odd-symmetric charge-flux characteristic has on the development of a particular dynamical behavior. It is proved how, driving the memristor with a sine-wave voltage source, the amplitude–angular frequency ratio selects a sub-class of observable current–voltage behaviors from the class of all possible dynamics, while the initial condition on flux specifies which of the behaviors in the sub-class is actually observed. In addition, a novel boundary condition-based model for memristor nano-scale films points out how specification of suitable dynamical behavior at film ends, depending on the particular physical realization under study and on driving conditions, crucially determines the observed dynamics.