【作者】 黄守芳；

【导师】 张季谦；

【作者基本信息】 安徽师范大学 ， 生物物理专业， 2018， 博士

【摘要】 近年来,随着复杂性、非线性科学的发展,复杂体系集体行为及演化规律的研究已成为科研工作们广泛关注的热点科研问题。复杂的耦合体系由于各个动力学单元通过各种方式相互作用而形成一个复杂系统,因而具有非常复杂的动力学行为,通过对相应参量的调控可以模拟部分实际体系的行为和功能。特别地,大脑神经网络是一个高度互联的复杂系统,可以表现出复杂网络的典型特征,它是通过所有神经元之间的众多突触(化学突触和缝隙连接)相互连接而形成的,其中任何神经元的活动都必然与神经元集体的组合活动有关。生物神经系统存在着丰富的合作行为及其转变,在神经系统的所有合作行为中,现有实验表明时空模式和同步动力学是非常关键的,通过这两种行为,神经系统可以对信息进行有效的处理和传输。因此,时空模式和同步(转变)已成为理论神经科学研究的热点。本论文通过理论模拟和计算机仿真,着重研究了随机因素(网络拓扑结构、外刺激信号、随机噪声信号以及延迟时间等)对复杂神经系统合作行为(时空模式和同步)的影响。主要工作和所得结论集中在以下几个方面:1、采用Hindmarsh-Rose(HR)神经元模型,研究实际生物细胞拓扑构型对耦合神经系统响应能力的影响。我们固定耦合强度,在耦合系统中的第一个神经元上加入(弱电流、噪声等)外部刺激,利用不同构型内部的耦合连接使得刺激可以扩散到整个系统。模拟结果显示:一方面,处于合适的拓扑结构时,系统会对较弱的电信号产生反应,表现出更好的反应能力;会减少噪声在内部传递的时滞,表现出更高的反应速度。另一方面,适当的拓扑结构还会提高神经系统同步能力和产生明显的选择效应。研究结果表明,耦合系统的拓扑结构在信号传播过程中起着重要的作用,可以帮助我们理解组织中细胞的协调和响应能力。相应的研究结果发表在Chinese Journal of Chemical Physics上。2、使用HR神经元模型,研究了非耦合细胞系统中的放电模式的同步行为。在这项工作中,膜电流被选为一个可控参数,所有细胞的电流初始值被随机地设置为接近某一分岔点。我们发现当没有外部刺激作用时,系统将呈现明显的非同步状态;当外刺激存在时,即使这些神经元之间没有任何耦合连接,也会出现完全同步,即出现了非耦合同步现象。并且,当这些神经元被设置为靠近其他周期模式的分岔点时,也可以观察到类似的行为。我们利用同步误差来讨论这种非耦合的同步行为。最后,发现这样的同步可能与不同细胞之间相位差的减小有内在的相关性。我们的研究结果表明,生物神经系统会在外部微弱刺激的帮助下实现非耦合同步模式,反过来,生物神经系统可以通过非耦合同步模式实现对外部微弱刺激的有效响应。相应的研究结果发表在Chinese Physics Letters上。3、以HR神经元细胞为单元构建耦合网络结构,利用混沌蚁群优化(CASO)算法研究网络同步动力学与最优耦合模式的关系,其中选择来自所有耦合配置的一些典型耦合网络进行分析。此外,为了进一步验证优化算法的结果,构建了42个单元的网络,计算出此网络的最优耦合矩阵,并且在优化和非优化耦合结构中比较了同步行为。我们的研究结果表明,通过CASO算法可以获得HR神经网络的合适的耦合矩阵。相应的研究结果发表在Nonlinear Dynamics上。4、使用HR模型研究时间延迟对神经网络中放电行为和去同步的影响。随着时间延迟的增加,神经网络表现出多样的放电行为,包括普通放电模式和放电模式转换(FPT)。与此同时,随着时间延迟的增加,神经系统中随着幅度减小的不稳定放电和放电的不同步性也在不断增强。此外,我们还研究了耦合强度和网络随机性对这些现象的影响。我们的研究结果意味着时间延迟可以诱发神经网络中的放电行为的转变现象、去同步和死振现象。这些发现为时间延迟在神经网络的合作活动中的作用提供了新的见解,并且可以帮助更好地理解神经系统中复杂的放电现象,以及时延增加引起的对脑功能的调控机制。相应的研究结果发表在Physica A上。5、使用HR模型考察外部刺激对耦合神经网络中时间延迟引发的放电行为和同步的影响。随着时间延迟的变化,我们发现神经网络呈现出多样的转变现象(包括FPT和同步转变),并且讨论了外部刺激强度和不同类型的刺激对这些现象的调控作用。研究结果表明刺激强度和刺激频率对神经网络中的FPT行为和同步转变具有重要的影响。包括改变神经系统FPT行为所需的临界值,并产生同步和去同步之间的新的转换模式。这些发现对于外部刺激在时滞神经网络的放电活动中的作用问题提供了新视角,同样可以帮助更好地理解复杂的时滞神经系统中的合作动力学行为。相应的研究结果投稿在Physics Letters A上。更多还原

【Abstract】 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’.更多还原