A discrete memristor model and its application in the Rulkov neuron

TL;DR

This paper introduces a discrete memristor model applied to a Rulkov chaotic neuron, demonstrating its impact on system dynamics, bifurcation behavior, and potential insights into neural memory and cognition.

Contribution

A novel discrete memristor model is integrated into the Rulkov neuron, revealing its effects on chaos control and neural dynamics, which was not previously explored.

Findings

Memristor charge influences bifurcation delay and fixed point emergence.

Increasing current magnification raises neuron discharge frequency.

Discrete memristor enhances Rulkov neuron performance and offers insights into neural memory.

Abstract

Continuous time memristor have been widely used in fields such as chaotic oscillating circuitsand neuromorphic computing systems, but research on the application of discretememristors haven't been noticed yet. In this paper, we designed a new chaoticneuron by applying the discrete model to two-dimensional Rulkov chaotic neuron,and analyzed its dynamical behaviors by extensive experiments involves phasediagram, bifurcation diagram, and spectral entropy complexity algorithm. The experimental results show that the charge of the memristor has an importanteffect on the system dynamics, delaying the occurrence of bifurcation, and evenin the case of full memory, leading to the disappearance of the bifurcation thus makethe system reach a fixed point. Besides, the increase of the current magnification,can also bring about the increase in discharge frequency ofneurons, and a wider and larger range of spectral entropy complexity. The results of our study show the performance of Rulkov chaotic neuronis improved by applying thediscrete memristor, and may provide new insights into the mechanism of memoryand cognition in the nervous.