Understanding and harnessing the internal physical mechanisms that govern memristive behavior is key to advancing their integration into neuromorphic computing systems. In this work, we present a modeling framework rooted in the concept of the chemical inductor [1], a reactive element originally discovered in ionic solar cells, adapted to describe memristive devices through a minimal model based on a single internal memory variable, x, governing the conductance state of the system. When x transitions between 0 and 1, it induces a low-to-high conductance change in the device, establishing a robust mechanism for generating hysteresis. This switching behavior is linked to a relaxation time governed by the chemical inductor, enabling control over the dynamic response of the system.

We illustrate this framework through an experimentally validated model of a memristive system based on a conical nanopore membrane embedded in an electrochemical cell. Static current-voltage measurements allowed the extraction of the stationary activation state of x, while impedance spectroscopy fitting to the minimal chemical inductor model yielded experimental values for the circuit elements. From these, we derived voltage-dependent relaxation times for the internal state—marking, the first experimental quantification of this property in a memristor. Building on these experimental insights, we developed a physically grounded dynamic model capable of reproducing both quasi-static I-V hysteresis and prototypical neuromorphic functions such as potentiation-depression measurements and paired-pulse facilitation, achieving excellent agreement with experimental data [2].

Building on this foundation, we extend the modeling framework to halide perovskite-based memristors. Experimental measurements have revealed the presence of additional capacitive features that cannot be captured by the single-variable memory model. To account for this, we incorporate an extra capacitive element that successfully reproduces the emergence of novel hysteretic responses at intermediate timescales, which are distinct from those governed by the primary activation variable x [3]. These observations point to more intricate internal dynamics that demand a refined modeling approach, capable of capturing the interplay between fast and slow processes in the system. Simultaneously, we are exploring the conditions under which halide perovskite memristors exhibit self-sustained oscillations, focusing on the emergence of negative differential resistance (NDR) as a key enabling feature [4]. Our models and early device-level simulations confirm that under specific voltage conditions, these systems can naturally transition into oscillatory regimes, offering a platform for integrated memristive oscillators.

In parallel, we are investigating the intrinsic noise characteristics of halide perovskite memristors. Our measurements indicate that fluctuations in resistance are closely linked to internal transitions in the system, suggesting a stochastic component in the evolution of internal states. Through noise spectral analysis and stochastic modeling, we are identifying correlations between noise signatures and switching dynamics. By embedding these memristors into simple oscillatory circuits, we demonstrate that intrinsic noise can act as a tuning parameter for driving transitions between oscillatory and non-oscillatory states. This controlled use of noise enables probabilistic switching behavior, laying the groundwork for noise-powered computational elements such as p-bits (probabilistic bits) [5]. These results underscore the potential of perovskite memristors not only as memory elements but also as fundamental building blocks for stochastic neuromorphic hardware.

Altogether, this body of work demonstrates how starting from a minimal modeling framework, based on internal memory variables and chemical inductive behavior, enables not only reproduction of experimental memristive responses but also the interpretation of complex functionalities. By progressively incorporating additional internal dynamics, noise sources, and non-linear phenomena, we bridge the gap between material-level understanding and emergent behaviors relevant for next-generation computing. This approach paves the way for leveraging memristive systems not only in conventional neuromorphic architectures such as oscillatory or spiking neural networks, but also in probabilistic and quantum-inspired platforms.