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.     

Chaotic phase synchronization in small-world networks of bursting neurons

We investigate the chaotic phase synchronization in a system of coupled bursting neurons in small-world networks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that phase synchronization is largely facilitated by a large fraction of shortcuts, but saturates when it exceeds a critical value. We also study the external chaotic phase synchronization of bursting oscillators in the small-world network by a periodic driving signal applied to a single neuron. It is demonstrated that there exists an optimal small-world topology, resulting in the largest peak value of frequency locking interval in the parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this interval increases with the driving amplitude, but decrease rapidly with the network size. We infer that the externally applied driving parameters outside the frequency locking region can effectively suppress pathologically synchronized rhythms of bursting neurons in the brain.     

Chaotic phase synchronization in a modular neuronal network of small-world subnetworks

We investigate the onset of chaotic phase synchronization of bursting oscillators in a modular neuronal network of small-world subnetworks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that this bursting synchronization transition can be induced not only by the variations of inter- and intra-coupling strengths but also by changing the probability of random links between different subnetworks. We also analyze the effect of external chaotic phase synchronization of bursting behavior in this clustered network by an external time-periodic signal applied to a single neuron. Simulation results demonstrate a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this synchronization region increases with the signal amplitude and the number of driven neurons but decreases rapidly with the network size. Considering that the synchronization of bursting neurons is thought to play a key role in some pathological conditions, the presented results could have important implications for the role of externally applied driving signal in controlling bursting activity in neuronal ensembles.     

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.     

Phase synchronization of bursting neural networks with electrical and delayed dynamic chemical couplings

Diffusive electrical connections in neuronal networks are instantaneous, while excitatoryor inhibitory couplings through chemical synapses contain a transmission time-delay.Moreover, chemical synapses are nonlinear dynamical systems whose behavior can bedescribed by nonlinear differential equations. In this work, neuronal networks withdiffusive electrical couplings and time-delayed dynamic chemical couplings are considered.We investigate the effects of distributed time delays on phase synchronization of burstingneurons. We observe that in both excitatory and Inhibitory chemical connections, the phasesynchronization might be enhanced when time-delay is taken into account. This distributedtime delay can induce a variety of phase-coherent dynamical behaviors. We also study thecollective dynamics of network of bursting neurons. The network model presents theso-called Small-World property, encompassing neurons whose dynamics have two time scales(fast and slow time scales). The neuron parameters in such Small-World network, aresupposed to be slightly different such that, there may be synchronization of the bursting(slow) activity if the coupling strengths are large enough. Bounds for the criticalcoupling strengths to obtain burst synchronization in terms of the network structure aregiven. Our studies show that the network synchronizability is improved, as itsheterogeneity is reduced. The roles of synaptic parameters, more precisely those of thecoupling strengths and the network size are also investigated.     

Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network

The spatiotemporal patterns and chaotic burst synchronization of a small-world neuronal network are studied in this paper. The synchronization parameter, similarity parameter and order parameter are introduced to investigate the dynamics behaviour of the neurons. Chaotic burst synchronization and nearly complete synchronization can be observed if the link probability and the coupling strength are large enough. It is found that with increasing link probability and the coupling strength chaotic bursts become appreciably synchronous in space and coherent in time, and the maximal spatiotemporal order appears at some particular values of the probability and the coupling strength, respectively. The larger the size of the network, the smaller the probability and the coupling strength are needed for the network to achieve burst synchronization. Moreover, the bursting activity and the spatiotemporal patterns are robust to small noise.     

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.     

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.     

电磁辐射诱发神经元放电节律转迁的动力学行为研究

本文首先根据能量转换理论建立了电磁辐射影响下神经元电流变量模型, 然后结合Hodgkin-Huxley(HH)神经元模型研究了电磁辐射对单个神经元以及耦合神经元放电行为的影响. 结果表明, 随着电磁辐射强度的增大, 神经元放电率逐渐减小, 最后达到一个比较稳定的值. 神经元原有的周期型放电由于辐射强度的增大而逐步过渡到簇放电状态, 并借助动态分岔理论解释了这种放电模式的转换. 同时证明了磁辐射对单个神经元放电的影响可以通过神经元间的耦合传递到临近其他神经元中.     

Taming desynchronized bursting with delays in the Macaque cortical network

Inhibitory coupled bursting Hindmarsh-Rose neurons are considered as constitutive units of the Macaque cortical network. In the absence of information transmission delay the bursting activity is desynchronized,giving rise to spatiotemporally disordered dynamics. This paper shows that the introduction of finite delays can lead to the synchronization of bursting and thus to the emergence of coherent propagating fronts of excitation in the space-time domain. Moreover,it shows that the type of synchronous bursting is uniquely determined by the delay length,with the transitions from one type to the other occurring in a step-like manner depending on the delay. Interestingly,as the delay is tuned close to the transition points,the synchronization deteriorates,which implies the coexistence of different bursting attractors. These phenomena can be observed by different but fixed coupling strengths,thus indicating a new role for information transmission delays in realistic neuronal networks.     

Bursting synchronization in clustered neuronal networks

Neuronal networks in the brain exhibit the modular (clustered) property, i.e., they are composed of certain subnetworks with differential internal and external connectivity. We investigate bursting synchronization in a clustered neuronal network. A transition to mutual-phase synchronization takes place on the bursting time scale of coupled neurons, while on the spiking time scale, they behave asynchronously. This synchronization transition can be induced by the variations of inter- and intra- coupling strengths, as well as the probability of random links between different subnetworks. Considering that some pathological conditions are related with the synchronization of bursting neurons in the brain, we analyze the control of bursting synchronization by using a time-periodic external signal in the clustered neuronal network. Simulation results show a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even in the presence of external driving. Hence, effective synchronization suppression can be realized with the driving parameters outside the frequency locking region.     

Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses

The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.     

The role of neural architecture and the speed of signal propagation in the process of synchronization of bursting neurons

Synchronized neuronal activity has been observed at all levels of human and any other nervous systems and was suggested as particularly relevant in information processing and coding. In the present paper we investigate the synchronization of bursting neuronal activity. Motivated by the fact that in neural systems the interplay between the network structure and the dynamics taking place on it is closely interrelated, we develop a spatial network representation of neural architecture in which we can tune the network organization between a scale-free network with dominating long-range connections and a homogeneous network with mostly adjacent neurons connected. Our results reveal that the most synchronized response is obtained for the intermediate regime where long- as well as short-range connections constitute the neural architecture. Moreover, the optimal response is additionally enhanced when the speed of signal propagation is optimized.     

Burst synchronization of electrically and chemically coupled map-based neurons

Burst synchronization and burst dynamics of a system consisting of two map-based neurons coupled through electrical or chemical synapses are discussed. Some basic characteristic quantities are introduced to describe burst synchronization and burst dynamics of neurons. It is observed that excitatory coupling leads to in-phase burst synchronization but inhibitory coupling results in anti-phase one. By using the basic characteristics of burst dynamics, the effects of the intrinsic bursting properties and the coupling schemes on complex bursting behaviors are also presented for both inhibitory and excitatory couplings. The results are instructive to identify bursting behaviors through experimental data.     

Goos-Hänchen effect of spin electron beams in a parallel double <Emphasis Type="Italic">δ</Emphasis>-barrier magnetic nanostructure

In this paper, we study the effect of time-periodic coupling strength (TPCS) and network connection degree ⟨k⟩ on the temporal coherence of the chaotic bursting of the scale-free networks of thermo-sensitive neurons. It is found that the chaotic bursting becomes ordered and can exhibit coherence resonance (CR) when TPCS amplitude ε ₀ or the network connection degree ⟨k⟩ is varied. In particular, the neuronal bursting may exhibit multiple CR (MCR) behavior when TPCS frequency ω is varied. It is also found that, as ⟨k⟩ is increased, the value of ε ₀ for the MCR decreases, but the frequency for the MCR almost keeps unchanged. These results show that the chaotic bursting can be tamed and the bursting temporal coherence can be enhanced and even optimized by TPCS and network connection degree. Furthermore, TPCS can repetitively enhance and even optimize the temporal coherence of the neuronal bursting behavior. These findings may help to better understand the roles of TPCS and network connection degree for improving the time precision of the information processing in neuronal networks.     

Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons

We study the dynamical states of a small-world network of recurrently coupled excitable neurons, through both numerical and analytical methods. The dynamics of this system depend mostly on both the number of long-range connections or "shortcuts", and the delay associated with neuronal interactions. We find that persistent activity emerges at low density of shortcuts, and that the system undergoes a transition to failure as their density reaches a critical value. The state of persistent activity below this transition consists of multiple stable periodic attractors, whose number increases at least as fast as the number of neurons in the network. At large shortcut density and for long enough delays the network dynamics exhibit exceedingly long chaotic transients, whose failure times follow a stretched exponential distribution. We show that this functional form arises for the ensemble-averaged activity if the failure time for each individual network realization is exponentially distributed.     

Burst synchronization transitions in a neuronal network of subnetworks

In this paper, the transitions of burst synchronization are explored in a neuronal network consisting of subnetworks. The studied network is composed of electrically coupled bursting Hindmarsh-Rose neurons. Numerical results show that two types of burst synchronization transitions can be induced not only by the variations of intra- and intercoupling strengths but also by changing the probability of random links between different subnetworks and the number of subnetworks. Furthermore, we find that the underlying mechanisms for these two bursting synchronization transitions are different: one is due to the change of spike numbers per burst, while the other is caused by the change of the bursting type. Considering that changes in the coupling strengths and neuronal connections are closely interlaced with brain plasticity, the presented results could have important implications for the role of the brain plasticity in some functional behavior that are associated with synchronization.     

Coherent periodic activity in excitatory Erdös-Renyi neural networks: the role of network connectivity

In this article, we investigate the role of connectivity in promoting coherent activity in excitatory neural networks. In particular, we would like to understand if the onset of collective oscillations can be related to a minimal average connectivity and how this critical connectivity depends on the number of neurons in the networks. For these purposes, we consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erdo?s-Renyi graph with average connectivity scaling as a power law with the number of neurons in the network. The scaling is controlled by a parameter γ, which allows to pass from massively connected to sparse networks and therefore to modify the topology of the system. At a macroscopic level, we observe two distinct dynamical phases: an asynchronous state corresponding to a desynchronized dynamics of the neurons and a regime of partial synchronization (PS) associated with a coherent periodic activity of the network. At low connectivity, the system is in an asynchronous state, while PS emerges above a certain critical average connectivity (c). For sufficiently large networks, (c) saturates to a constant value suggesting that a minimal average connectivity is sufficient to observe coherent activity in systems of any size irrespectively of the kind of considered network: sparse or massively connected. However, this value depends on the nature of the synapses: reliable or unreliable. For unreliable synapses, the critical value required to observe the onset of macroscopic behaviors is noticeably smaller than for reliable synaptic transmission. Due to the disorder present in the system, for finite number of neurons we have inhomogeneities in the neuronal behaviors, inducing a weak form of chaos, which vanishes in the thermodynamic limit. In such a limit, the disordered systems exhibit regular (non chaotic) dynamics and their properties correspond to that of a homogeneous fully connected network for any γ-value. Apart for the peculiar exception of sparse networks, which remain intrinsically inhomogeneous at any system size.     

一类位于加周期分岔中的貌似混沌的随机神经放电节律的识别

识别非周期神经放电节律是混沌还是随机一直是一个重要的科学问题. 在神经起步点实验中发现了一类介于周期k和周期k+1(k=1,2)节律之间非周期自发放电节律, 其行为是长串的周期k簇和周期k+1簇的交替. 确定性理论模型Chay模型展示出了周期k和周期k+1节律的共存行为. 噪声在共存区诱发出了与实验结果类似的非周期节律, 说明该类节律是噪声引起的两类簇的跃迁. 非线性预报及其回归映射揭示该节律具有确定性机理; 将两类簇分别转换为0和1得到一个二进制序列, 对该序列进行概率分析获得了两类簇跃迁的随机机理. 这不仅说明该节律是具有确定性结构的随机节律而不是混沌, 还为深入识别现实神经系统的混沌和随机节律提供了典型示例和有效方法.     

Spatial patterns in a network composed of neurons with different excitabilities induced by autapse

It has been identified that autapse can modulate dynamics of single neurons and spatial patterns of neuronal networks. In the present paper, based on the results that autapse can induce type II excitability changed to type I excitability, spatial pattern transitions are simulated in a two-dimensional neuronal network composed of excitatory coupled neurons with autapse which can induce excitability transition. Different spatial patterns including random-like pattern, irregular wave, regular wave, and nearly synchronous behavior are simulated with increasing the percentage (σ) of neurons with type I excitability. When noise is introduced, spiral waves are induced. By calculating signal-to-noise ratio from the spatial structure function and the mean firing probability of neurons, regular waves and spiral waves exhibit optimal spatial correlation, implying the occurrence of spatial coherence resonance phenomenon. The changes of mean firing probability of neurons show that different firing frequency between type I excitability and type II excitability may be an important factor to modulate the spatial patterns. The results are helpful to understand the spatial patterns including spiral waves observed in the biological experiment on the rat cortex perfused with drugs which can induce single neurons changed from type II excitability to type I excitability and block the inhibitory couplings between neurons. The excitability transition, absence of inhibitory coupling, noise as well as the autapse are important factors to modulate the spatial patterns including spiral waves.