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

A discrete memristor model and its application in the Rulkov neuron