The Integral Role of Coupling Memristors in Complex Firing Patterns

This paper proposes a novel concept in memristive devices termed “Coupling Memristor (CM)”, aiming to unveil its potential application for modeling complicated neuron circuits and generating complex patterns of oscillations such as bursting in conjunction with other linear, nonlinear or memristive devices. It is well known that traditional Uncoupled Memristor (UM) functions solely based on its inherent properties, while the concept of CM proposed in this paper shares the characteristics of other devices. This study investigates the dynamics of CM and its potential applications in advanced modeling of neuromorphic systems. This work also provides evidence that the small-signal model of a memristor conventionally modeled with the series connection of inductors-resistors and paralleled by another resistor without depending on the interconnected coefficients parameters is only valid when all the states are directly related to the state-dependent Ohm’s law. However, missing one or more states in state-dependent Ohm’s law introduces additional dependencies and feedback effects that require complex modeling techniques for the analysis of the memristor’s small-signal model. Additionally, this work demonstrates from the Chay–Keizer pancreatic [Formula: see text]-cell, Phantom Bursting Model (PBM)-II and Chay neuron model of an excitable cell, that the slow dynamics, which communicate with fast dynamics, are in fact a slow modulation CM. It plays a significant role in changing the cell membrane of pancreatic [Formula: see text]-cells and excitable cells, thereby facilitating the emergence of bursting patterns, which is an essential mechanism for insulin secretion in pancreatic [Formula: see text]-cell. This fundamental principle has the potential to revolutionize the design of new memristive devices and enable precise modeling of neurons, thus fostering comprehensive investigations in neuromorphic systems. The concepts of CM explored in the applications in pancreatic [Formula: see text]-cells, PBM-II and excitable cells provide an accurate modeling and a deeper understanding of neuron dynamics. This study could contribute to the development of novel tools for the treatment of neurons, metabolism, and insulin-related disorders.