场耦合忆阻神经网络的电活动

神经元之间除了突触耦合，还存在磁通耦合.因此在传统的神经元模型中引入磁通量，并研究场耦合下神经网络的放电活动具有实际意义.建立一个含场耦合的Hodgkin-Huxley忆阻神经网络，引入神经元节点之间的距离权重，用磁通量描述时变电磁场，采用磁控忆阻器实现膜电位和磁通量之间的耦合.探讨距离权重和系统大小对神经网络放电活动的影响.研究发现，随着权重增大，神经网络放电活动增强，且系统规模越大，诱导神经元兴奋性的权重阈值越大，系统大小不影响神经网络活性随距离权重变化的规律.在不同的权重值下，神经网络活性随系统大小变化的规律明显不同.研究表明，距离权重和系统大小对含场耦合的忆阻神经网络放电活动有重要影响，其中距离权重起主导作用.     

电磁场耦合忆阻Izhikevich神经网络电活动研究

考虑到电磁场的影响,在Izhikevich神经元模型中引入电场变量和磁通变量,利用电突触耦合构建神经网络,研究电磁场耦合忆阻Izhikevich神经网络集体动力学行为。数值仿真发现：随着电突触耦合强度的增大,神经网络逐渐达到同步状态,并且神经元的放电模式也会随之改变。增大磁场耦合值可以提高神经元的放电活性,并且对网络同步也有一定的促进作用,而增大电场则会抑制神经元的放电活动。另外,当电突触与磁场耦合共同作用时,磁场耦合值越小,电突触耦合更能有效促进网络同步;在电突触耦合强度的作用下,电场抑制电活动的效果更明显。研究结果可望为理解神经系统中的信号编码和传递提供新的见解。     

耦合Hindmarsh-Rose神经元的放电模式和完全同步

通过数值模拟和分岔分析的方法研究了Hindmarsh-Rose（HR）神经元的放电模式。当外加直流激励变化时，单个的神经元表现为静息态、周期性峰放电、周期性簇放电以及混沌的放电模式。利用快慢动力学分析的方法研究了HR神经元的动力学行为。当每个神经元表现为静息态、周期性放电和混沌时，两个耦合的神经元在一定的耦合强度下均会达到完全同步。神经元的耦合方式模拟神经元之间缝隙连接的电耦合。理论分析了完全同步的判断准则，并给出相应的数值模拟结果。电耦合HR神经元耦合系统的峰峰间期的分岔结构在耦合的作用下仍然能保持未耦合时的分岔结构。     

忆阻Rulkov神经网络同步研究

研究电突触、化学突触以及两者共存对忆阻Rulkov神经模型集体动力学行为的影响。对于两个忆阻Rulkov神经元系统,各种耦合方式都能使系统实现同步。对于不同的耦合强度,神经元呈现不同的放电模式,如方波,三角波,脉冲放电等。当电突触、化学突触同时存在时,系统的同步更依赖于电耦合强度。对全局耦合忆阻Rulkov神经网络同步的研究表明：化学突触单独作用时,同步发生在耦合参数的某个区域范围,当化学耦合强度超过某一阈值时,同步会随着耦合强度的增加而被破坏。电突触单独作用时,系统很快到达同步状态,并且电耦合强度是决定神经元处于静止还是峰放电的关键因素,随着电耦合强度增加,神经元放电频率、振幅增大。当电、化学耦合同时存在时,耦合强度的增加使神经元由静息转变为圆弧放电,并进入同步状态。本文提供了一种通过调整耦合方式和耦合强度,控制神经网络放电模式及其同步的可能方法。     

最小神经元模型放电起始动态控制与分析

本文采用最小神经元模型,从生理学角度设计wash-out滤波器,实现了不同放电起始动态机理之间的转换,并证明wash-out滤波器控制通过影响阈下电流的竞争结果改变了神经元的放电起始动态机理. 关键词： 放电起始动态机理 阈下电流竞争 最小神经元模型 wash-out滤波器     

基于KTP晶体的斯塔克啁啾快速绝热通道波长转换

通过近似类比原子绝热布居理论,建立了基于KTP晶体的斯塔克啁啾快速绝热通道理论的波长转换模型,系统研究了晶体耦合调制中的耦合迟延参数和宽度参数、泵浦强度、温度、入射波长等因素对转换效率的影响.结果表明在KTP晶体中能实现入射光能量到出射光能量近乎完全的转换,同时转换过程中中间光能量保持极低.离最优晶体耦合调制参数越远,转换效率越低.转换效率先随泵浦强度的增大不断增大,当转换效率达到最大值,增大泵浦强度对转换效率几乎无影响.温度和入射波长的变化对转换效率影响较小.研究结果表明基于KTP晶体的斯塔克啁啾快速绝热通道理论的波长转换具有很好的鲁棒性.该研究可为紫外到中红外光源的获取以及光子器件的制造提供理论依据.     

具有时滞的抑制性自突触诱发的神经放电的加周期分岔

神经放电节律在神经系统功能实现中起着重要的作用.具有自突触(起始和结束于同一细胞的突触)的神经元普遍存在于神经系统,本文研究了单神经元模型在抑制性自突触作用下的放电节律.结果发现,随着时滞和/或耦合强度的增加,可以诱发Rulkov神经元模型放电节律的加周期分岔.随着放电节律的周期数的增加,平均放电频率增大,当时滞和/或耦合强度大于某一阈值时,频率大于没有自突触时的放电频率.用快慢变量分离方法可以获得没有自突触的神经放电节律的分岔结构,可用于认识外界负向脉冲诱发的新节律.这些新的节律模式与加周期分岔中的节律模式一致.研究结果不仅揭示了抑制性自突触可以诱发典型的非线性现象——加周期分岔,还给出了抑制性自突触可以提高放电频率的新现象,与以前的自突触压制放电的观点不同,进一步丰富了对抑制性自突触诱发的非线性现象的认识.     

“Hopf/homoclinic”簇放电和“SubHopf/homoclinic"簇放电之间的同步

以修正过的Morris-Lecar神经元模型为例,讨论了“Hopf/homoclinic”簇放电和“SubHopf/homoclinic"簇放电之间的同步行为.首先,分别考察了同一拓扑类型的两个耦合簇放电神经元的同步行为,发现“Hopf/homoclinic”簇放电比“SubHopf/homoclinic”簇放电达到膜电位完全同步所需要的耦合强度小,即前者比后者更容易达到膜电位完全同步.其次,对这两个不同拓扑类型的簇放电神经元的耦合同步行为进行了讨论.通过数值分析发现随着耦合强度的增加,两种不同类型的簇放电首先达到簇放电同步,然后当耦合强度足够大时甚至可以达到膜电位完全同步,并且同步后的放电类型更接近容易同步的簇放电类型,即“Hopf/homoclinic”簇放电.然而令人奇怪的是此时慢变量并没有达到完全同步,而是相位同步;慢变量之间呈现为一种线性关系.这一点和现有文献的结果截然不同.     

Hindmarsh-Rose神经元的随机自共振和噪声影响下的同步

研究了噪声对Hindmarsh-Rose(HR)神经元随机自共振和同步的影响。将高斯白噪声加入HR神经元模型的膜电位上，把外界直流电作为分岔参数，分别考虑参数处于Hopf分岔前、Hopf分岔附近和Hopf分岔后时，噪声影响下的随机自共振现象。两个未经耦合的全同HR神经元，如果接受相同的噪声激励，只要噪声强度高于某临界值，就能达到完全同步。进一步，噪声能够增强弱耦合神经元的完全同步。数值结果表明簇放电的神经元比峰放电的神经元更容易被噪声诱导而达到完全同步，耦合也增强了神经元对噪声激励的灵敏度。     

基于麦克斯韦电磁场理论的神经元动力学响应与隐藏放电控制

钙、钾、钠等离子在细胞内连续泵送和传输时产生的时变电场不仅会影响神经元的放电活动,而且会诱导时变磁场去进一步调节细胞内离子的传播.根据麦克斯韦电磁场理论,时变的电场和磁场在细胞内外的电生理环境中会相互激发而产生电磁场.为了探究电磁场影响下的神经元放电节律转迁,本文在三维Hindmarsh-Rose(HR)神经元模型的基础上,引入磁通变量和电场变量,建立了一个五维HR神经元模型(简称EMFN模型).首先,结合Matcont软件分析了EMFN模型的平衡点分布与全局分岔性质,发现并分析了该模型存在的亚临界Hopf分岔、隐藏放电及其周期放电与静息态共存等现象.其次,利用双参数及单参数分岔、ISI分岔和最大Lyapunov指数等工具进行数值仿真,详细分析了EMFN模型存在的伴有混沌及无混沌的加周期分岔结构、混合模式放电和共存模式放电等现象,同时揭示了电场和磁场强度影响其放电节律的转迁规律.最后,利用Washout控制器将EMFN模型的亚临界Hopf分岔转化为超临界Hopf分岔,使其在分岔点附近的拓扑结构发生改变,由此达到消除其隐藏放电的目的.本文的研究结果证实了新建神经元模型具有丰富的放电节律,将影响神经元的信息传递和编码,为完善神经元模型,揭示电磁场对生物神经系统的影响,以及探求一些神经性疾病的致病机理提供了思路.     

Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay

The firing of a neuron model is mainly affected by the following factors:the magnetic field, external forcing current, time delay, etc. In this paper, a new time-delayed electromagnetic field coupled dual Hindmarsh-Rose neuron network model is constructed. A magnetically controlled threshold memristor is improved to represent the self-connected and the coupled magnetic fields triggered by the dynamic change of neuronal membrane potential for the adjacent neurons. Numerical simulation confirms that the coupled magnetic field can activate resting neurons to generate rich firing patterns, such as spiking firings, bursting firings, and chaotic firings, and enable neurons to generate larger firing amplitudes. The study also found that the strength of magnetic coupling in the neural network also affects the number of peaks in the discharge of bursting firing. Based on the existing medical treatment background of mental illness, the effects of time lag in the coupling process against neuron firing are studied. The results confirm that the neurons can respond well to external stimuli and coupled magnetic field with appropriate time delay, and keep periodic firing under a wide range of external forcing current.     

动态突触、神经耦合与时间延迟对神经元发放的影响

神经元膜电位的受激发放在神经系统的信息传递中起着重要作用.基于一个受动态突触刺激的突触后神经元发放模型,采用数值模拟和傅里叶变换分析的方法研究了动态突触、神经耦合与时间延迟对突触后神经元发放的影响.结果发现:突触前神经元发放频率与Hodgkin-Huxley神经元的固有频率发生共振决定了突触后神经元发放的难易,特定频率范围内的电流刺激有利于神经元激发,动态突触输出的随机突触电流中这些电流刺激所占的比率在很大程度上影响了突触后神经元的发放次数;将突触后神经元换成神经网络后,网络中神经元之间的耦合可以促进神经元的发放,耦合中的时间延迟可以增强这种促进作用,但是不会改变神经耦合对神经元发放的促进模式.     

Dynamical response of a neuron–astrocyte coupling system under electromagnetic induction and external stimulation

Previous studies have observed that electromagnetic induction can seriously affect the electrophysiological activity of the nervous system. Considering the role of astrocytes in regulating neural firing, we studied a simple neuron–astrocyte coupled system under electromagnetic induction in response to different types of external stimulation. Both the duration and intensity of the external stimulus can induce different modes of electrical activity in this system, and thus the neuronal firing patterns can be subtly controlled. When the external stimulation ceases, the neuron will continue to fire for a long time and then reset to its resting state. In this study, "delay" is defined as the delayed time from the firing state to the resting state, and it is highly sensitive to changes in the duration or intensity of the external stimulus. Meanwhile, the self-similarity embodied in the aforementioned sensitivity can be quantified by fractal dimension. Moreover, a hysteresis loop of calcium activity in the astrocyte is observed in the specific interval of the external stimulus when the stimulus duration is extended to infinity, since astrocytic calcium or neuron electrical activity in the resting state or during periodic oscillation depends on the initial state. Finally, the regulating effect of electromagnetic induction in this system is considered. It is clarified that the occurrence of "delay" depends purely on the existence of electromagnetic induction. This model can reveal the dynamic characteristics of the neuron–astrocyte coupling system with magnetic induction under external stimulation. These results can provide some insights into the effects of electromagnetic induction and stimulation on neuronal activity.     

Bursting and spiking due to additional direct and stochastic currents in neuron models

Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to spiking, induced by additional direct and stochastic currents, are explored in rest states corresponding to two values of the parameter $V_{\rm K}$ in the Chay neuron system. Three cases are considered by numerical simulation and fast/slow dynamic analysis, in which only the direct current or the stochastic current exists, or the direct and stochastic currents coexist. Meanwhile, several important bursting patterns in neuronal experiments, such as the period-1 ``circle/homoclinic" bursting and the integer multiple ``fold/homoclinic" bursting with one spike per burst, as well as the transition from integer multiple bursting to period-1 ``circle/homoclinic" bursting and that from stochastic ``Hopf/homoclinic" bursting to ``Hopf/homoclinic" bursting, are investigated in detail.     

Stochastic resonance and synchronization behaviors of excitatory-inhibitory small-world network subjected to electromagnetic induction

The phenomenon of stochastic resonance and synchronization on some complex neuronal networks have been investigated extensively.These studies are of great significance for us to understand the weak signal detection and information transmission in neural systems.Moreover,the complex electrical activities of a cell can induce time-varying electromagnetic fields,of which the internal fluctuation can change collective electrical activities of neuronal networks.However,in the past there have been a few corresponding research papers on the influence of the electromagnetic induction among neurons on the collective dynamics of the complex system.Therefore,modeling each node by imposing electromagnetic radiation on the networks and investigating stochastic resonance in a hybrid network can extend the interest of the work to the understanding of these network dynamics.In this paper,we construct a small-world network consisting of excitatory neurons and inhibitory neurons,in which the effect of electromagnetic induction that is considered by using magnetic flow and the modulation of magnetic flow on membrane potential is described by using memristor coupling.According to our proposed network model,we investigate the effect of induced electric field generated by magnetic stimulation on the transition of bursting phase synchronization of neuronal system under electromagnetic radiation.It is shown that the intensity and frequency of the electric field can induce the transition of the network bursting phase synchronization.Moreover,we also analyze the effect of magnetic flow on the detection of weak signals and stochastic resonance by introducing a subthreshold pacemaker into a single cell of the network and we find that there is an optimal electromagnetic radiation intensity,where the phenomenon of stochastic resonance occurs and the degree of response to the weak signal is maximized.Simulation results show that the extension of the subthreshold pacemaker in the network also depends greatly on coupling strength.The presented results may have important implications for the theoretical study of magnetic stimulation technology,thus promoting further development of transcranial magnetic stimulation(TMS) as an effective means of treating certain neurological diseases.     

Parameter-dependent synchronization transition of coupled neurons with co-existing spiking and bursting

A firing pattern transition is simulated in the Leech neuron model, firstly from bursting to co-existence of spiking and bursting and then to spiking. The attraction domain of spiking and bursting for three different parameter values are calculated. Synchronization transition processes of two coupled Leech neurons, one is bursting and the other the co-existing spiking, are simulated for the three parameters. The three synchronization processes appear similar as the coupling strength increases, beginning from non-synchronization to complete synchronization through a complex dynamical procedure, but their detailed processes are different depending on the parameter values. The transition procedure is complex and the complete synchronization is in bursting for larger parameter values, while the process is simple with complete synchronization of spiking for smaller values. The potential relationship between complete synchronization and the attraction domain is also discussed. The results are instructive to understanding the synchronization behaviors of the coupled neuronal system with co-existing attractors.     

Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse

Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh-Rose (HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval (ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic (A-periodic) bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.     

Pre-B?tzinger复合体的从簇到峰放电的同步转迁及分岔机制

Pre-Bötzinger复合体是兴奋性耦合的神经元网络,通过产生复杂的放电节律和节律模式的同步转迁参与调控呼吸节律.本文选用复杂簇和峰放电节律的单神经元数学模型构建复合体模型,仿真了与生物学实验相关的多类同步节律模式及其复杂转迁历程,并利用快慢变量分离揭示了相应的分岔机制.当初值相同时,随着兴奋性耦合强度的增加,复合体模型依次表现出完全同步的“fold/homoclinic”,“subHopf/subHopf”簇放电和周期1峰放电.当初值不同时,随耦合强度增加,表现为由“fold/homoclinic”,到“fold/fold limit cycle”、到“subHopf/subHopf”与“fold/fold limit cycle”的混合簇放电、再到“subHopf/subHopf”簇放电的相位同步转迁,最后到反相同步周期1峰放电.完全(同相)同步和反相同步的周期1节律表现出了不同分岔机制.反相峰同步行为给出了与强兴奋性耦合容易诱发同相同步这一传统观念不同的新示例.研究结果给出了preBötzinger复合体的从簇到峰放电节律的同步转迁规律及复杂分岔机制,反常同步行为丰富了非线性动力学的内涵.     

Ordered bursting synchronization and complex wave propagation in a ring neuronal network

Ordered bursting synchronization and complex propagation are investigated for a ring neuronal network in which each neuron exhibits chaotic bursting behaviour. The neurons become more and more synchronous in chaotic bursting as the synaptic strength is increased. It is shown that excitatory chemical synapses can effectively tame the chaos, and ordered bursting synchronization can be observed as the synaptic strength is further increased. However, synchronization among neurons is weakened as the number of neurons is increased. More importantly, it is shown that ordered bursting synchronization can be turned into spiking synchronization at certain noise intensity. Complex spatio-temporal patterns propagating towards both sides of pacemaker are found in this network before the emergence of spiking synchronization.