The Regulation Of Firing Rhythms Of Nervous System Based On Locally Active Memristors

Neurons are the basic unit that constitutes the nervous system.Studying the firing behavior of neurons helps to develop a neuromorphic system with neurological functions,and can explain some physiological diseases and cognitive impairments in humans.In recent years,memristors have been widely used in neural circuits due to their nanoscale,nonlinearity,non-volatility,and programmability.The locally active memristor is a special kind of memristor,which is highly similar to the structure and characteristics of biological synapses.Therefore,this paper has done the following work based on the locally active memristors.1.A Hindmarsh–Rose model based on the four-stable memristor is constructed,and its firing behaviors and regulation of firing rhythms are analyzed.Firstly,we propose a four-stable locally active memristor.Then,its coexisting hysteresis loops,non-volatility,and locally active characteristic under different initial values are analyzed,and a circuit model of the memristor is built to validate its characteristics.A Hindmarsh-Rose neuron model based on the memristor is constructed,and the dynamical behaviors and regulation of the firing rhythms of the memristor-based neuron under different initial values are studied.Since the memristor itself has four stable states,the regulation of the four firing modes can be achieved by changing the initial value of the memristor in the four steady-state regions.The regulation of firing rhythms in this article is regional adjustable,simpler,and easier to realize compared with the previous methods.2.The coupled Hindmarsh–Rose and Fitz Hugh–Nagumo nervous systems are constructed based on a bi-stable memristor,and the regulation of firing rhythms and phase synchronization are analyzed by using the traditional dynamic analysis methods.Firstly,a bi-stable locally active memristor with a simple structure is constructed,and its characteristics are studied.A coupled nervous system composed of Hindmarsh–Rose and Fitz Hugh–Nagumo neurons is built using the memristor synapse.Firstly,the equilibria and its stability are analyzed,and it is found that the distribution of the equilibria is complex,so the coupled neural system can exhibit abundant firing behaviors.Then,we analyze the bifurcation diagram and Lyapunov exponents by varying the coupling strength under two sets of initial values.When the coupling strength keeps unchanged,the bifurcation diagram and the attraction basin under different initial values of the memristor are presented,and we find that the firing rhythms of the neural system are closely dependent on the coupling strength and initial conditions.Finally,the phase synchronization of the neural system under different coupling strengths is analyzed,the coupled neural system can achieve phase synchronization or even complete synchronization by increasing the coupling strength.