Relationship Between Switching-Resistor Memristor Models and Chua’s Ideal Memristor

Determine how the memristor model that switches between two distinct memductance values (i.e., a nonlinear resistor switching between two conductance states) relates to Chua’s ideal flux-controlled memristor characterized by the flux–charge relation q = \hat{q}(\varphi) with strictly passive memductance; specify the precise correspondence, if any, between these two modeling frameworks for neural network interconnections.

Background

The paper establishes almost-convergence for neural networks whose interconnections are implemented with ideal memristors in the sense of Chua’s model, where the memductance is a strictly passive, state-dependent conductance derived from a smooth flux–charge relation. This framework underpins the main results by enabling a cooperative reduced-order description via the Flux-Charge Analysis Method.

The authors note that a separate branch of literature analyzes neural networks using a fundamentally different memristor model: a nonlinear resistor that switches between two discrete memductance values. As highlighted by Pershin and Di Ventra (2020), the formal relationship between this switching-resistor model and Chua’s ideal memristor remains unclear. Clarifying this relationship is important to understand whether results proved under the ideal memristor framework transfer to systems modeled with switching memductances, and to unify stability and convergence analyses across memristor-based neural network models.