Brayton-Moser mixed potential extends to memristor circuits via flux-charge analysis

In a breakthrough for circuit theory, researchers from the University of Siena have extended the classic Brayton-Moser mixed potential concept—originally developed in 1964 for nonlinear RLC circuits—to circuits containing memristors. The key challenge was that memristors are inherently flux-charge devices, not voltage-current ones. The team's work, published on arXiv (2606.04638), introduces a mixed potential for a class of RLCM circuits (resistors, inductors, capacitors, and memristors) by operating entirely in the flux-charge domain. They establish an equivalence principle via flux-charge analysis (FCAM), showing that an RLCM circuit in the flux-charge domain behaves like a nonlinear RLC circuit in the traditional voltage-current domain. This allows the mixed potential to be defined compactly. Explicit examples include Chua's circuit with a memristor and large-scale memristor arrays with a neural architecture, demonstrating practical applicability.

A companion paper by the same authors uses this newly formulated mixed potential to derive Lyapunov-like results on the convergence of RLCM circuits. This is particularly significant because existing convergence theories did not cover the simultaneous presence of capacitors and inductors in a memristor circuit. The mixed potential provides a systematic framework to write state equations in a compact form and analyze stability. For professionals designing neuromorphic hardware, analog AI accelerators, or next-generation memory, this work offers a rigorous theoretical foundation to predict circuit behavior, ensure convergence, and avoid oscillations in complex memristor networks. It bridges a critical gap between abstract circuit theory and practical memristor-based systems.