Research On The Effect Of Structural Diversity On The Dynamics Of Neural System

In recent years,with the continuous deepening of research on the complex and non-linear problems of complex systems,it has been found that the dynamic behavior of complex systems must not only be affected by the random factors of the external environment,but also be regulated by the intrinsic factors of the system.This is mainly reflected in the fact that,on the one hand,the system itself has topological complexity that leads to the complexity of the system function.On the other hand,the dynamic behavior of complex systems in nature is often affected by various random disturbances,including internal and external noise,topological disorder,structural diversity,and so on.Two factors make the nonlinear system achieve certain functions under certain conditions.The most common is topological disorder to tame the chaos,random disturbances can regulate the synchronization and coherence behavior in the system and so on.As we all know,there are many complex systems in the nature that can be described by the network,especially the neural network system composed of neurons as nodes.People have found that the topology of the network determines the characteristics and functions of the network,and the interaction between network nodes and the stimuli in the internal and external environment will regulate the dynamic behavior of the system.In most studies of neural networks,neurons are often treated asidentical nodes connected to the network.In fact,even with the same type of neuronal cells,there will be some differences between individuals due to their size,shape,location in the network,and the intensity and type of external stimulus.In theoretical research,people use the difference in one or more parameters in a model or equation to express differences between individuals.This difference between individuals is called diversity.In this dissertation,the neuronal system was used as the research object,and the regulation of the neuron cell structure dynamics was investigated.These results will help us further study the dynamic mechanism of the neuronal system under real conditions.In the first part of the paper,we introduced the basic knowledge related to nonlinear science and neuron systems related to the dissertation,including relevant knowledge of nonlinear dynamical systems,bifurcation and chaos,structure and function of neurons,neuronal dynamics model,neural network dynamic behavior,diversity.In the second part of the paper,on one hand,we studied the effects of diversity on neuronal bifurcation characteristics and found that for neuron systems under certain coupling conditions,selecting appropriate diversity parameter values can reduce the neuronal bifurcation threshold,and indicating that appropriate diversity can effectively enhance the ability of neuron coupling systems to respond to external stimuli.Not only that,the parameters of the adjustment system,the couplingstrength,and the size of the neural network system can effectively improve this response capability.On the other hand,we also found that the diversity of structural parameters can induce random resonance in neural networks,which helps to improve the ability of neural networks to respond to weak signals.And the closer the choice of bifurcation parameter value is to the bifurcation point,the higher the resonance peak,the better the system's response to external signals.This work has been published in the journal "Biophysics".In the third part of the paper,we studied the effects of diversity on neuronal firing patterns using HH neurons as research subjects.The diversity as an unordered source can lead to an orderly state in the collective behavior of complex systems.This mechanism also exists in the coupled system of HH neurons with certain differences of the same kind.The study found that with the increase of diversity,the HH neurons shift from excitable discharge patterns to periodic peak discharge patterns,indicating that diversity can induce phase transition behavior in HH neuronal networks.This work has been published in the journal "Biophysics".In order to further study the regulatory role of diversity in different systems,we recently tried to do some preliminary work in the memristive neural system.Based on the memristor model of a new type of window function proposed by us,the relevant parameters in the memristor model are adjusted and the variation of the volt-amperecharacteristic curve is studied.In the future,based on this work,we will introduce diversity into the memristive neural network to examine its influence and the regulatory mechanismon the dynamical behavior of memristive neural networks.This work has been submitted to the journal "Inter.J of Bifurcation and Chaos".The last part of the paper summarizes the above research work and looks forward to future research.This dissertation only examines the effect of topology parameter diversity on neuronal bifurcation characteristics,resonance phenomena,phase transitions,and synchronization behavior.In fact,in a real neural network,not only there are many different coupling modes,but also various environmental factors,which cause complex systems to produce complex and diverse states such as periodic states,chaotic states,and singular states,etc.The diversity in these aspects will certainly have a certain influence on the dynamic behavior of the system and its regulation and control.These will all be further studied in the future.