Synchronization transition in gap-junction-coupled leech neurons

Real neurons can exhibit various types of firings including tonic spiking, bursting as well as silent state, which are frequently observed in neuronal electrophysiological experiments. More interestingly, it is found that neurons can demonstrate the co-existing mode of stable tonic spiking and bursting, which depends on initial conditions. In this paper, synchronization in gap-junction-coupled neurons with co-existing attractors of spiking and bursting firings is investigated as the coupling strength gets increased. Synchronization transitions can be identified by means of the bifurcation diagram and the correlation coefficient. It is illustrated that the coupled neurons can exhibit different types of synchronization transitions between spiking and bursting when the coupling strength increases. In the course of synchronization transitions, an intermittent synchronization can be observed. These results may be instructive to understand synchronization transitions in neuronal systems.     

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.     

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.     

Spiking sychronization regulated by noise in three types of Hodgkin—Huxley neuronal networks

In this paper,we study spiking synchronization in three different types of Hodgkin-Huxley neuronal networks,which are the small-world,regular,and random neuronal networks.All the neurons are subjected to subthreshold stimulus and external noise.It is found that in each of all the neuronal networks there is an optimal strength of noise to induce the maximal spiking synchronization.We further demonstrate that in each of the neuronal networks there is a range of synaptic conductance to induce the effect that an optimal strength of noise maximizes the spiking synchronization.Only when the magnitude of the synaptic conductance is moderate,will the effect be considerable.However,if the synaptic conductance is small or large,the effect vanishes.As the connections between neurons increase,the synaptic conductance to maximize the effect decreases.Therefore,we show quantitatively that the noise-induced maximal synchronization in the Hodgkin-Huxley neuronal network is a general effect,regardless of the specific type of neuronal network.     

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.     

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.     

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.     

Bursting synchronization in non-locally coupled maps

Neuron activity presents two timescales, a fast one related to action-potential spiking, and a slow timescale in which bursting takes place. Bursting activity in neuron ensembles can be synchronized, meaning the adjustment of the bursting phases due to coupling. We investigated bursting synchronization in a non-locally coupled lattice using a two-dimensional map to describe neuron activity. The coupling involves all sites in a lattice, the corresponding strength decreasing with the lattice distance in a power-law fashion. We observed bursting synchronization for wide intervals of the coupling parameters. We also investigated the bursting synchronization of the ensemble with an external time-periodic signal applied to one or more selected neurons.     

Network mechanism for burst generation

We report on the mechanism of burst generation by populations of intrinsically spiking neurons, when a certain threshold in coupling strength is exceeded. These ensembles synchronize at relatively low coupling strength and lose synchronization at stronger coupling via spatiotemporal intermittency. The latter transition triggers fast repetitive spiking, which results in synchronized bursting. We present evidence that this mechanism is generic for various network topologies from regular to small-world and scale-free ones, different types of coupling and neuronal model.     

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。     

Coherence resonance and synchronization of Hindmarsh-Rose neurons with noise

Noise effects on coherence resonance and synchronization of Hindmarsh-Rose (HR) neuron model are studied. The coherence resonance of a single HR neuron with Gaussian white noise added to the membrane potential is investigated in situations before, near and after the Hopf bifurcation, separately, with the external direct current as a bifurcation parameter. It is shown that even though there is no coupling between neurons, uncoupled identical HR neurons driven by a common noise can achieve complete synchronization when the noise intensity is higher than a critical value. Furthermore, noise also enhances complete synchronization of weakly coupled neurons. It is concluded that synchronization in bursting neurons is easier to be induced than in spiking ones, and coupling enhances the sensitivity of synchronization of neurons to noise stimulus.     

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.     

Phase synchronization in ensembles of bursting oscillators

We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles.     

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.     

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.     

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.     

Power law behavior related to mutual synchronization of chemically coupled map neurons

The widely represented network motif, constituting an inhibitory pair of bursting neurons, is modeled by chaotic Rulkov maps, coupled chemically via symmetrical synapses. By means of phase plane analysis, that involves analytically obtaining the curves guiding the motion of the phase point, we show how the neuron dynamics can be explained in terms of switches between the noninteracting and interacting map. The developed approach provides an insight into the observed time series, highlighting the mechanisms behind the regimes of collective dynamics, including those concerning the emergent phenomena of partial and common oscillation death, hyperpolarization of membrane potential and the prolonged quiescence. The interdependence between the chaotic neuron series takes the form of intermittent synchronization, where the entrainment of membrane potential variables occurs within the sequences of finite duration. The contribution from the overlap of certain block sequences embedding emergent phenomena gives rise to the sudden increase of the parameter characterizing synchronization. We find its onset to follow a power law, that holds with respect to the coupling strength and the stimulation current. It is established how different types of synaptic threshold behavior, controlled by the gain parameter, influence the values of the scaling exponents.     

Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh--Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.     

Synchronization and coherence resonance in chaotic neural networks

Synchronization and coherence of chaotic Morris--Lecar (ML) neural networks have been investigated by numerical methods. The synchronization of the neurons can be enhanced by increasing the number of the shortcuts, even though all neurons are chaotic when uncoupled. Moreover, the coherence of the neurons exhibits a non-monotonic dependence on the density of shortcuts. There is an optimal number of shortcuts at which the neurons' motion is most ordered, i.e. the order parameter (the characteristic correlation time) that is introduced to measure the coherence of the neurons has a maximum. These phenomena imply that stochastic shortcuts can tame spatiotemporal chaos. The effects of the coupling strength have also been studied. The value of the optimal number of shortcuts goes down as the coupling strength increases.