Nonlinear Dynamics and Invariants of Motion in ReRAM Cells

Abstract

Memristor circuits are gaining increasing importance in modern electronics due to their ability to mimic neurons, synapses, and, more generally, the computation capabilities of biological neural systems. The ideal memristor model was introduced by L. Chua in a seminal paper back in 1971. Later on, several more complex memristor models, such as the popular Voltage ThrEshold Adaptive Memristor model, have been developed to better describe the state‐dependent current‐voltage behavior of physical memristor devices, in particular Resistive Random Access Memories, a nanotechnology of great appeal nowadays. While the study of circuits with ideal memristors is reaching a mature state, very few results are available on the analysis of the dynamics of circuits with real memristors. As demonstrated in this paper, peculiar dynamical properties of cells with ideal memristors are also displayed by some analogue electrical circuits with real memristors. In particular, simple circuits, including, as dynamical elements, one capacitor and a memristive one‐port, composed of a pair of back‐to‐back Resistive Random Access Memory devices described through the Voltage ThrEshold Adaptive Memristor model, admit physical quantities, referred to as Invariants of Motion, which are conserved over time. As a consequence, their state space can be foliated into Invariant Manifolds, which induce the coexistence of infinitely many different monostable and bistable quiescent steady states. A second‐order cell from the proposed class may be toggled between regimes of quiescent monostability and bistability by controlling the initial condition‐dependent index of the manifold along which its dynamical variables are constrained to lie at all times. Moreover, at any equilibrium point, the voltage across its capacitor vanishes, which allows the memristive one‐port to hold its state without energy consumption. These attractive properties make the proposed cells ideal candidates to serve as sensing‐and‐memcomputing units for innovative Cellular Neural Networks to be deployed for solving time‐critical edge computing problems in resource‐constrained environments.