Spiral Wave in Small-World Networks of Hodgkin-Huxley Neurons

The effect of small-world connection and noise on of Hodgkin-Huxley neurons are investigated in detail. Some the formation and transition of spiral wave in the networks interesting results are found in our numerical studies, i） The quiescent neurons are activated to propagate electric signal to others by generating and developing spiral wave from spiral seed in small area. ii） A statistical factor is defined to describe the collective properties and phase transition induced by the topology of networks and noise, iii） Stable rotating spiral wave can be generated and keeps robust when the rewiring probability is below certain threshold, otherwise, spiral wave can not be developed from the spiral seed and spiral wave breakup occurs for a stable rotating spiral wave. iv） Gaussian white noise is introduced on the membrane of neurons to study the noise-induced phase transition on spiral wave in small-world networks of neurons. It is confirmed that Ganssian white noise plays active role in supporting and developing spiral wave in the networks of neurons, and appearance of smaller factor of synchronization indicates high possibility to induce spiral wave.     

Instability and Death of Spiral Wave in a Two-Dimensional Array of Hindmarsh-Rose Neurons

Spiral wave could be observed in the excitable media, the neurons are often excitable within appropriate parameters. The appearance and formation of spiral wave in the cardiac tissue is linked to monomorphic ventricular tachycardia that can denervate into polymorphic tachycardia and ventricular fibrillation. The neuronal system often consists of a large number of neurons with complex connections. In this paper, we theoretically study the transition from spiral wave to spiral turbulence and homogeneous state （death of spiral wave） in two-dimensional array of the Hindmarsh-Rose neuron with completely nearest-neighbor connections. In our numerical studies, a stable rotating spiral wave is developed and selected as the initial state, then the bifurcation parameters are changed to different values to observe the transition from spiral wave to homogeneous state, breakup of spiral wave and weak change of spiral wave, respectively. A statistical factor of synchronization is defined with the mean field theory to analyze the transition from spiral wave to other spatial states, and the snapshots of the membrane potentials of all neurons and time series of mean membrane potentials of all neurons are also plotted to discuss the change of spiral wave. It is found that the sharp changing points in the curve for factor of synchronization vs. bifurcation parameter indicate sudden transition from spiral wave to other states. And the results are independent of the number of neurons we used.     

Robustness,Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block

The development of spiral wave in a two-dimensional square array due to partial ion channel block (Potas- sium, Sodium) is investigated, the dynamics of the node is described by Hodgkin-Huxley neuron and these neurons are coupled with nearest neighbor connection. The parameter ratio x Na (and xK ), which defines the ratio of working ion channel number of sodium (potassium) to the total ion channel number of sodium (and potassium), is used to measure the shift conductance induced by channel block. The distribution of statistical variable R in the two-parameter phase space (parameter ratio vs. poisoning area) is extensively calculated to mark the parameter region for transition of spiral wave induced by partial ion channel block, the area with smaller factors of synchronization R is associated the parameter region that spiral wave keeps alive and robust to the channel poisoning. Spiral wave keeps alive when the poisoned area (potassium or sodium) and degree of intoxication are small, distinct transition (death, several spiral waves coexist or multi-arm spiral wave emergence) occurs under moderate ratio x Na (and xK ) when the size of blocked area exceeds certain thresholds. Breakup of spiral wave occurs and multi-arm of spiral waves are observed when the channel noise is considered.     

Study Under AC Stimulation on Excitement Properties of Weighted Small-World Biological Neural Networks with Side-Restrain Mechanism

In this paper,we propose a new model of weighted small-world biological neural networks based on biophysical Hodgkin-Huxley neurons with side-restrain mechanism.Then we study excitement properties of the model under alternating current (AC) stimulation.The study shows that the excitement properties in the networks are preferably consistent with the behavior properties of a brain nervous system under different AC stimuli,such as refractory period and the brain neural excitement response induced by different intensities of nolse and coupling.The results of the study have reference worthiness for the brain nerve electrophysiology and epistemological science.     

Multi-mode Spiral Wave in a Coupled Oscillatory Medium

Multi-mode spiral wave and its breakup in 1-d and 2-d coupled oscillatory media is studied here by theoretic analysis and numerical simulations. The analysis in 1-d system shows that the dispersion relation curve could be nonmonotonic depending on the coupling strength. It may also lead to the coexistence of different wave numbers within one system. Direct numerical observations in 1-d and 2-d systems conform to the prediction of dispersion relation analysis. Our findings indicate that the wave grouping can also be observed in oscillatory media without tip meandering and waves with negative group velocity can occur without inhomogeneity.     

Phase Transitions of an Epidemic Spreading Model in Small-World Networks

We propose a modified susceptible-infected-refractory-susceptible (SIRS) model to investigate the global oscillations of the epidemic spreading inWatts-Strogatz (WS) small-world networks. It is found that when an individual immunity does not change or decays slowly in an immune period, the system can exhibit complex transition from an infecting stationary state to a large amplitude sustained oscillation or an absorbing state with no infection. When the immunity decays rapidly in the immune period, the transition to the global oscillation disappears and there is no oscillation. Furthermore, based on thespatio-temporal evolution patterns and the phase diagram, it is disclosed that a long immunity period takes an important role in the emergence of the global oscillation in small-world networks.     

Dynamics of Spiral Wave Tip in Excitable Media with Gradient Parameter

Using a Barkley model as an example, we study spirM waves and spiral tips in a gradient excitable medium. The gradient distribution of parameters is introduced to depict the inhomogeneous medium. It is found that the parameter fluctuations play an important role in the morphology of spiral pattern and the movements of spiral tips. For varied gradient parameters, it is observed that there exist three kinds of spiral behaviors, stable rotation, rebound of spiral tip from the boundary, and spiral breakup.     

Suppression of Spiral Wave in Modified Orengonator Model

In this paper, a spatial perturbation scheme is proposed to suppress the spiral wave in the modified Orengonator model, which is used to describe the chemical reaction in the light-sensitive media. The controllable external illumination Ф is perturbed with a spatial linear function. In our numerical simulation, the scheme is investigated by imposing the external controllable illumination on the space continuously and/or intermittently. The numerical simulation results confirm that the stable rotating spiral wave still can be removed with the scheme proposed in this paper even if the controllable Ф changed vs. time and space synchronously. Then the scheme is also used to control the spiral wave and turbulence in the modified Fitzhugh-Nagumo model. It is found that the scheme is effective to remove the sable rotating and meandering spiral wave but it costs long transient period and intensity of the gradient parameter to eliminate the soiral turbulence.     

脑功能激活光诱发机理小世界网络分析研究

研究光诱发和静息两种状态下的脑功能网络的信息传输枢纽、网络聚合能力和信息传输的最小路径的差异性。采用小世界网络理论对脑功能网络进行建模,通过对脑功能网络连接度、簇系数和最小路径进行分析,得出光诱发状态下的信息传输重要枢纽为岛叶、后扣带回功能区;丘脑、海马两处功能网络有较大聚合能力。光诱发过程从额上回经颞中回传输到枕中回。静息状态下的信息传输重要枢纽为楔叶、舌回;中央旁小叶、颞上回脑功能网络有较大聚合能力。静息状态下的左半区最佳信息传输路径为左额上回、左颞中回、右楔叶最后到左枕中回;右脑半区的为右额上回、右前扣带回、左枕下回最后到右枕中回。光诱发状态与静息状态的最佳传输路径有明显的区别。     

Suppression of Spiral Wave in Modified Orengonator Model

In this paper, a spatial perturbation scheme is proposed to suppress the spiral wave in the modified Orengonator model, which is used to describe the chemical reaction in the light-sensitive media. The controllable external illumination Φ is perturbed with a spatial linear function. In our numerical simulation, the scheme is investigated by imposing the external controllable illumination on the space continuously and/or intermittently. The numerical simulation results confirm that the stable rotating spiral wave still can be removed with the scheme proposed in this paper even if the controllable Φ changed vs. time and space synchronously. Then the scheme is also used to control the spiral wave and turbulence in the modified Fitzhugh-Nagumo model. It is found that the scheme is effective to remove the sable rotating and meandering spiral wave but it costs long transient period and intensity of the gradient parameter to eliminate the spiral turbulence.     

两阶段脉冲控制螺旋波的数值模拟

提出两种两阶段的螺旋波控制方法,第一阶段用正相脉冲力作用快变量,第二阶段用反相脉冲力作用快变量或用正相脉冲力作用慢变量,用修改后的Bär模型进行数值模拟,结果表明:两阶段的脉冲控制方法比单阶段控制方法更有效地控制螺旋波,作用力可以减少到后者力大小的38%~55%.结果建议,可以通过两阶段控制螺旋波的方法改进心脏电除颤.     

Spiral Waves and Multiple Spatial Coherence Resonances Induced by Colored Noise in Neuronal Network

Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bifurcation on invariant circle,coupled to its nearest neighbors by electronic coupling.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity.By calculating spatial structure function and signal-to-noise ratio(SNR),it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered,respectively.SNR manifest multiple local maximal peaks,indicating that the colored noise can induce multiple spatial coherence resonances.The maximal SNR values decrease as the correlation time of the noise increases.These results not only provide an example of multiple resonances,but also show that Gaussian colored noise play constructive roles in neuronal network.     

Dynamics of Spiral Wave Tip in Excitable Media with Gradient Parameter

Using a Barkley model as an example, we study spiral waves and spiral tips in a gradient excitable medium. The gradient distribution of parameters is introduced to depict the inhomogeneous medium. It is found that the parameter fluctuations play an important role in the morphology of spiral pattern and the movements of spiral tips. For varied gradient parameters, it is observed that there exist three kinds of spiral behaviors, stable rotation, rebound of spiral tip from the boundary, and spiral breakup.     

Destruction of Spiral Wave Using External Electric Field Modulated by Logistic Map

Evolution of spiral wave generated from the excitable media within the Barkley model is investigated. The external gradient electric field modulated by the logistic map is imposed on the media （along x- and y-axis）. Drift and break up of spiral wave are observed when the amplitude of the electric field is modulated by the chaotic signal from the logistic map, and the whole system could become homogeneous finally and the relevant results are compared when the gradient electric field is modulated by the Lorenz or Rossler chaotic signal.     

Drive Control of Spiral Wave and Turbulence by a Target Wave in CGLE

Suppression of spiral wave and turbulence in the complex Ginzburg-Landau equation (CGLE) plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the proposed drive-response system, which consists of two coupled CGLEs, is investigated and controlled by a state error feedback controller with the lattice Boltzmann method. First, spiral wave and turbulence are, respectively, generated by selecting appropriate parameters of the response system under the no-flux boundary and perpendicular gradient initial conditions. Then, based on the random initial condition, the target wave yielded by introducing spatially localized inhomogeneity into the drive system is applied on the above response system. The numerical simulation results show that the spiral wave and turbulence existing in the response system could be successfully eliminated by the target wave in the drive system during a short evolution time. Furthermore, it turns out that the transient time for the drive course is related to the control intensity imposed on the whole media.     

Evolution of Spiral Waves in Excitable Systems

Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of Duan＇s topological current theory, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.     

小世界网络中的量子纠缠渗流

本文研究了小世界复杂网络中的长程量子纠缠态的制备。提出了量子纠缠渗流优化网络量子通信的方案。通过在经典纠缠渗流协议(CEP)中引入局域化的"target-swap"量子操作,形成量子纠缠渗流协议(QEP)。研究表明QEP在长程纠缠制备的效能方面明显优于CEP,通过度分布变化的分析解释了QEP具有优势的原因。     

单向耦合神经元网络中螺旋波的自发形成机制

构造一个具有单向耦合的二维神经元网络,引入信息传输熵来描述定向信息传输,采用Hindmarsh-Rose神经元模型研究网络中螺旋波等有序波自发产生的机制.数值模拟表明：适当选取耦合的强度和单向耦合的距离,网络可自发出现螺旋波、行波、靶波和平面波.各种有序波的产生与网络中出现信息间歇定向传输有关,网络出现单或多螺旋波时发生熵共振现象.噪声、抑制性耦合和排斥性耦合诱发螺旋波时网络中也存在信息间歇定向传输.首次发现自维持长平面波,其存在是由于网络存在持续的强信息定向传输.     

Excitation Properties of the Biological Neurons with Side-Inhibition Mechanism in Small-World Networks

We have studied the excitation properties of biophysical Hodgkin-Huxley neurons with the side-inhibition mechanism in small-world networks. The result shows that the excitation properties in the networks are preferably consistent with the characteristic properties of a brain neural system under external constant stimuli, such as fatigue effect, extreme excitation principle, and the brain neural excitation response induced by different in- tensity of noise and coupling. The results of the study might shed some light on the study of the brain nerve electrophysiology and epistemological science.     

螺旋波动力学性质的元胞自动机有向小世界网络研究

以Greenberg-Hastings激发介质元胞自动机模型为基础,研究了有向小世界网络中重新连接概率p对螺旋波动力学行为的影响.对于在规则网络下的稳定螺旋波,施加有向小世界网络后发现:当p值较小时,原本稳定的螺旋波仍保持其稳定性.随着p的增大,先后观察到螺旋波持续漫游、螺旋波断裂以及螺旋波消失等现象.通过监测系统的激发比率,发现以上现象的产生源于介质激发性随p的增大而降低.同时还发现元胞周期的变化也与p有关. 关键词： 元胞自动机 螺旋波 激发介质 有向小世界网络