Nonlinear Dynamics And Synchronization Of Discrete Memristive Rulkov Neurons And Neural Networks

Biological neurons are the basic unit of information processing in the brain.Each neuron is connected to other 10~2-10~4 neurons through synapses,forming a neural network with extremely complex topology and function.At present,neuron models in the form of discrete maps have attracted extensive attention because of their high computational efficiency,simple models,large time steps required for each iteration,and the ability to capture important dynamics and characteristics of neuron activities.Existing studies have shown that the study of nonlinear dynamics analysis and synchronous control of memristive neural network is of great significance for understanding the signal encoding and propagation mechanism of the nervous system.There are not many simultaneous studies.On the other hand,complex networks have attracted attention due to their wide applications in different scientific fields such as biology and engineering.For this reason,based on complex network theory,this paper introduces discrete Hewlett-Packard(HP)memristors into two-dimensional Rulkov chaotic neurons by using mathematical modeling methods,establishes discrete memristive Rulkov chaotic neurons,and analyzes discrete The nonlinear dynamic behavior of memristive Rulkov neural network,and the synchronization of the network is controlled by adjusting parameters.The thesis research is divided into two parts:one is to derive the discrete memristive Rulkov chaotic neuron model and analyze its dynamic behavior;the other is to realize the synchronous control of the neural network by adjusting the parameters.The specific research content of this paper is as follows:(1)Summarize the research background and significance of this paper,then introduce the research status of discrete neurons,synchronous control of nervous system and memristor application,and finally briefly introduce the basic theoretical knowledge related to complex network and memristor model,which provides a basis for this paper theoretical support.(2)The dynamical behavior in discrete memristive Rulkov neurons is studied.First,the classical continuous HP memristor is deduced into a discrete HP memristor by mathematical theory,and the hysteresis loop proves that the discrete HP memristor conforms to the three important characteristics of the generalized memristor.Then,the discrete HP memristor is introduced into the two-dimensional Rulkov neuron to establish the discrete memristor Rulkov neuron.Finally,using numerical simulation method,its dynamic behavior is analyzed by bifurcation diagram,phase diagram and spectral entropy complexity algorithm.The findings demonstrate that employing discrete memristors can improve the performance of Rulkov neurons and may provide new insights into the mechanisms of memory and cognition in the nervous system.(3)The collective dynamic behavior and synchronization control of globally coupled memristive Rulkov neural network are studied.Firstly,a single neuron model and a globally coupled memristive Rulkov neural network model considering both electrical and chemical synapses are established.Using the methods of numerical simulation and statistical analysis,the synchronous analysis of a single neuron is performed first,and then the globally coupled Rulkov memristive neural network is analyzed.The research results show that the electrical synaptic coupling strength and chemical synaptic coupling strength play an important role in regulating the firing behavior and synchronous behavior of neural networks,and provide useful guidance for the study of signal propagation between neurons.(4)The effect of NW small-world connection topology on the synchronization of memristive Rulkov neural network is studied.Synchronous analysis of memristor Rulkov neural networks with different connection topological probabilities p and system parametersα,based on memristive Rulkov neural networks considering electrical and chemical synaptic coupling,through timing diagrams,spatio-temporal patterns,temporal snapshots and error functions.The research results show that the topological probability in the small-world network has an important influence on regulating the dynamic behavior of the neural network,and provides a topology and system parameter values that are most conducive to system synchronization.