Research On The Regulatory Mechanism Of Random Factors On Cooperative Dynamics In Neural Systems

In recent years,with the development of complexity and nonlinear science,the research on collective behavior and evolution of complex systems has been the focus of the academic field.The coupling systems are the complex systems because of the interaction of various dynamic units through various ways.Therefore,they have very complex dynamic behaviors.the behavior and function of some actual systems could be simulated by controlling the the corresponding parameters.In particular,The neural network in our human being brain is a highly interconnected complex system,in which the activity in any neuron is necessarily related to the combined activity of collective neurons.Neural systems can exhibit the typical features of complex networks,which is formed via interconnection of thousands of synapses?chemical synapses and electrical gap junctions?among all neurons.There exist rich cooperative behaviors and their transitions in biological neuronal systems.Among all of cooperative behaviors of neural systems,the existing experiments have shown that the spatiotemporal pattern and synchronization dynamics are very crucial,through which the efficient processing and transmission of information can be conducted across the nervous system.Resultantly,the spatiotemporal patterns and synchronization have become currently a hot research topic in theoretical neuroscience.Through theoretical and computer simulation,this dissertation focuses on the influence of stochastic factors?network topology,external stimuli and time delay?on the cooperative behavior?spatial-temporal patterns and synchronization?of complex neural systems.The main work contents and conclusions are focused as following:1?The effect of realistic topology configuration of intercellular connections on the response ability in coupled cell system is numerically investigated by using the Hindmarsh-Rose?HR?model.For the proper coupling intensity,we set the control parameter to be near the critical value,and the external stimulus is introduced to the first cell in coupled system.It is found that,on one hand,when the cells are coupled with some proper topological structures,the external stimulus could transmit through the system,and shows better response ability and higher sensitivity.On the other hand,the influence of topological configuration on the synchronous ability and selection effect of neural system are also discussed.Our results display that the topology of coupled system may play an important role in the process of signal propagation,which could help us to understand the coordinated performance of cells in tissue.The works of this part have been published in the journal'Chinese Journal of Chemical Physics'.2?Using the model of HR neurons,we study the synchronous behavior of the firing patterns in an uncoupled cell system.In this work,the membrane current_ext is selected as a controllable parameter,whose initial values for allcells are set to be near one of the bifurcation points randomly.It is found that the system will show un-synchronous state when the external stimuli is absent,otherwise,full synchrony will appear,even though without any coupling connection among theseneurons,indicating the occurrence of uncoupled synchrony.Moreover,similar behavior could also be observed when these neurons are set to be near other bifurcation points.The synchronous error is calculated for discussing this uncoupled synchrony behavior.Finally,we find that such synchrony may have some inherent relevance with the decrease of phase difference between different cells.Our results suggest that biological neuron systems may achieve an effective response to external feeble stimulus by the mode of uncoupled synchrony instead of only by the coupled scheme.The works of this part have been published in the journal'Chinese Physics Letters'.3?To research the relationship between network synchronous dynamics and the optimal coupling mode,we have constructed the coupled network structure with the HR neuron cells as the unit and found out the optimal coupling matrix,by using the chaos ant swarm optimization?CASO?algorithm.Some typical coupled networks from all the coupled configurations are selected for analysis.Furthermore,to further verify the results of the optimization algorithm,a network of 42 cell units is constructed and the synchronization behavior is compared in both the optimization and non-optimized coupling topology.Our results indicate that proper coupling matrix of HR neural network could be obtained by means of CASO algorithm.The works of this part have been published in the journal'Nonlinear Dynamics'.4?We used the HR model to study the effect of time delay on the transition of firing behaviors and desynchronization in neural networks.As time delay is increased,neural networks exhibit diversity of firing behaviors,including regular spiking or bursting and firing patterns transitions?FPTs?.Meanwhile,the desynchronization of firing and unstable bursting with decreasing amplitude in neural system,are also increasingly enhanced with the increase of time delay.Furthermore,we also studied the effect of coupling strength and network randomness on these phenomena.Our results imply that time delays can induce transition and desynchronization of firing behaviors in neural networks.These findings provide new insight into the role of time delay in the firing activities of neural networks,and can help to better understand the firing phenomena in complex systems of neural networks.A possible mechanism in brain that can cause the increase of time delay is discussed.The works of this part have been published in the journal'Physica A'.5?We used the Hindmarsh-Rose model to study the effect of external stimulus on the time delay induced firing behaviors and synchronization in N coupled neural networks.As time delay is changed,neural networks exhibit diversity of firing behaviors.We di scussed the effect of external stimulus intensity and different types of stimuli on these phenomena.Our results imply that both stimulus intensity and stimulus frequency have a non-trivial impact on firing patterns transitions?FPTs?behaviors and synchronization transitions in neural networks.Including changing the critical value of time delay-induced FPT behavior and generating new mode of transitions between synchronization and desynchronization.These findings provide new insight into the role of external stimulus in the firing activities of neural networks with time delay,and can help to better understand the firing phenomena in complex systems of neural networks.The works of this part have been submitted to the journal'Physics Letters A'.