The Characteristics Of Memristor And Edge Of Chaos Research Based On Hodgkin-Huxley Cardiac Purkinje Fiber Model

With the rapid development of science and technology,humans look forward to exploring the rules of life intelligence and providing new ideas for the development of artificial intelligence and computer science by study brain,the complex network.Hodgkin-Huxley model is a mathematical model that measures the physical activity of the Atlantic squid,which is a classic quantitative model in numerous neural network models.The memristor has long been considered as a "missing" important component,which has the characteristics of small volume,large storage,low energy consumption,memory and similar with synapses.The memristor also show the independent learning and weight plasticity in artificial neural network.Chaos,as an important concept in nonlinear science,is known as one of the three scientific discoveries of the twentieth century,which explains the transition between order and randomness from a scientific way.The edge of chaos is a manifestation of the spontaneous adjustment of the complex nervous system and the transient existence of the nonlinearity.The main research contents of this paper include:(1)Taking Cardiac Hodgkin-Huxley Purkinje Fiber model as research object,we found that the potassium channel and sodium channel have different strength of characteristics of memristor.Then,we design the circuit structure of a first order potassium ion memristor and a second order sodium ion memristor and perturbation equivalent memristor circuit based on the equilibrium point of potassium ion and sodium ion.(2)According to the mathematical definition of edge of chaos,we divide the activity state of the model is divided into three main areas: locally active domain,locally passive domain and the edge of chaos domain.Study the changes of waveform and heart rhythm in three regions,we can inference the cardiac state is normal,dangerous,chaos or static.Delineating the safe range of normal heartbeat,and migrating,extending or shrinking the edge of chaos domain by external force.(3)Combining the characteristics of cellular neural network,analyzing the variation of the waveform of the heart Purkinje fiber induced by the interaction between cells,for the change of discrete Laplace reaction-diffusion coefficient,we achieve an orderly,stable or chaotic trend of the overall neural network system to effectively control and guide the normal activities of the nervous system.This study extends the neural network applied in the field of nonlinear dynamics,provides certain theoretical basis to explore the complex human nervous system activity especially to the health heart.