Research On Nonlinear Dynamic And Control Of Biological Neurons And Networks

Biological neurons,as the basis of the nervous system that produces cognitive functions such as sensory,learning,memory,and thinking,have unparalleled importance in information optimization and processing,and understanding of the memory rules of the brain.It is an important subject of research at home and abroad.As a multi-level super-large information network,the biological neural network is also the most complex non-linear dynamic system currently,an in-depth study of its non-linear dynamics has important theoretical value for revealing the process,cognition,and thinking mechanism of brain neural information transmission.Research on chaotic neurons and neural networks provides a dynamic method for exploring various self-organizing processes in the brain,such as thinking,learning,feeling,memory,and invention.In the past two decades,theory and application of complex network have received widespread attention in many scientific and technical fields,such as chemistry,physics,biology,sociology,etc.The complex biological neural network system composed of a large number of neurons has always been an interesting and important research topic.In this paper,the research on the nonlinear dynamic behavior and control of biological neurons and neural networks mainly includes three aspects: the first is the effect of memory state on the nonlinear dynamics of discrete neuron models;Second,to study the influence of the connection topology and coupling strength of complex neural networks on their discharge behavior;the third is based on LaSalle invariant set theorem and Lyapunov stability theory,chaos control is performed on Hindmarsh-Rose(HR)and Morris–Lecar(ML)neurons with magnetic field memristion.The main research work of the paper is as follows:(1)Introduction: Introducing the research background and significance of this subject,and briefly describes some special network structure models such as the Hodgkin Huxley(HH)model,ML model,and HR model.(2)Briefly introduce the basic theory and network structure of complex biological neural networks,and explore the generation and properties of memristors,which will pave the way for subsequent research.(3)The effects of memory state on the nonlinear dynamics of discrete neuron models are studied,the memory effect characteristics are determined by two memory parameters,? and?.The study found that for the first type of memory,the larger the value of parameter?,the larger the system parameters of the first bifurcation of the neuron,that memory delays the first bifurcation of a neuron.In particular,when the memory parameter ?=1,the bifurcation disappears and the system converges to the stable point of the neuron.For memory parameter?,there are two opposite dynamic trends in the neuron model.When ?? ?5.00,as the memory factor increases,the chaotic region shrinks and eventually disappears.However,when?(27)15.0 ?,as the memory factor increases,chaos regenerates,and the chaotic area gradually increases.Research results show that memory has an important influence on the dynamic behavior of discrete neuron models.(4)The influence of connection topology and coupling strength of complex neural networks on their discharge behavior was studied.Firstly,the new man watts(NW)small world neural network is established with the HH neuron with magnetic coupling memristor as the node and the connection between the neurons as the edge,then study the neural network discharge pattern by changing the connection topology probability and coupling strength.The results show that for a given coupling strength,when the connection topology probability is small,the neural network has no discharge behavior;When the connection topology probability is greater than the threshold,neurons in the network will discharge,and with the further increase of the connection topology probability p,the discharge intensity becomes greater.Research results show that connection topology probability p can induce and enhance electrical activity of neural networks.Our research is expected to provide useful insights into the collective dynamics of truly coupled neurons.(5)Based on LaSalle's invariant set theorem and Lyapunov stability theory,a new chaos control method is proposed to control chaos for memristive HR an ML neurons with magnetic fields.And use numerical simulation to verify the correctness and effectiveness of the control method.The advantage of this control method is that the controller does not depend on the system model and system parameters,and it is still effective when the position of the neuron equilibrium point is unknown.The results are helpful for understanding the information processing,memory and abnormal discharge of brain neurons by the human brain.