A simple current-controlled second-order memristor model and its third neuronal circuit implementation
TL;DR
This paper proposes a simple current-controlled second-order LAM mathematical model, which exhibits both negative differential resistance edge of chaos (EOC) domains and positive differential resistance (PDR) EOC domains, and constructs a minimalist third-order neuronal circuit by simply paralleling the LAM with a capacitor.
Abstract
Memristors are promising core components for neuromorphic computing, offering a path to surpass the von Neumann bottleneck through their high efficiency and low power consumption. Among them, locally-active memristors (LAMs) play a crucial role in emulating neuronal dynamics, as the edge of chaos (EOC) domain is essential for generating action potentials. However, existing second-order memristor models often involve complex mathematical expressions, which severely limits theoretical analysis and application research. To this end, this paper proposes a simple current-controlled second-order LAM mathematical model, which exhibits both negative differential resistance (NDR) edge of chaos (EOC) domains and positive differential resistance (PDR) EOC domains. Leveraging this model, we construct a minimalist third-order neuronal circuit by simply paralleling the LAM with a capacitor. Dynamics analysis reveals that the circuit exhibits diverse neuronal firing patterns in the NDR-based EOC domains, including periodic spiking, chaotic oscillations, and bursting behavior, while only periodic spiking occurs in the PDR-based EOC domains. The proposed approach is validated by hardware experiments, providing a novel and efficient solution for implementing complex neuronal circuits.