White noise-induced spiral waves and multiple spatial coherence resonances in a neuronal network with type I excitability

White noise-induced pattern formation is studied in a network composed of Morris–Lecar neuronal models with type I excitability and with initial values higher than that of the resting potential. The appearance and disappearance of spiral waves, as well as the transitions between spiral wave patterns with different kinds of complexity characterized by the normalized spatial autocorrelation function, enable changes in the order of the network so as to exhibit a scenario with two or more locally maximal peaks, as can be clearly seen in the signal to noise ratio curves, as the noise intensity is adjusted from small to large in a wide range. A possible physical mechanism of the multiple resonances based on the dynamics of type I excitability and initial values is provided. The potential biological significance of the noise-induced spiral waves is discussed.     

Observation of stochastic resonance near a subcritical bifurcation

A hysteretic Subcritical period-doubling bifurcation is observed in the nonlinear strain dynamics of a magnetostrictive oscillator. The dynamic strain response of the magnetostrictive oscillator was observed with a high-resolution fiber optic interferometer. The effects of low-frequency modulation and band-limited stochastic fluctuations on such a bifurcation are investigated. Power spectral density measurements show that for an optimal value of externally injected noise the signal-to-noise ratio of a low-frequency modulation signal is enhanced by greater than 14 dB, thus indicating the first experimental observation of stochastic resonance near a bistable period-doubling bifurcation.     

Multiple coherence resonance induced by time-periodic coupling in stochastic Hodgkin-Huxley neuronal networks

In this paper, we study the effect of time-periodic coupling strength (TPCS) on the spiking coherence of Newman-Watts small-world networks of stochastic Hodgkin-Huxley (HH) neurons and investigate the relations between the coupling strength and channel noise when coherence resonance (CR) occurs. It is found that, when the amplitude of TPCS is varied, the spiking induced by channel noise can exhibit CR and coherence bi-resonance (CBR), and the CR moves to a smaller patch area (bigger channel noise) when the amplitude increases; when the frequency of TPCS is varied, the intrinsic spiking can exhibit CBR and multiple CR, and the CR always occurs when the frequency is equal to or multiple of the spiking period, manifesting as the locking between the frequencies of the intrinsic spiking and the coupling strength. These results show that TPCS can greatly enhance and optimize the intrinsic spiking coherence, and favors the spiking with bigger channel noise to exhibit CR. This implies that, compared to constant coupling strength, TPCS may play a more efficient role for improving the time precision of the information processing in stochastic neuronal networks.     

Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency (wave number) of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.     

双稳态系统中随机共振和相干共振的相关性

研究了加性噪声和乘性噪声共同驱动的双稳态系统中的随机共振和相干共振现象. 针对加性噪声和乘性噪声之间不存在关联性和存在关联性两种情形, 引入一种适当的能同时表征随机共振和相干共振的指标, 应用一阶欧拉方法, 通过数值模拟对系统的随机共振和相干共振现象进行研究. 结果表明在弱噪声驱动下, 随着加性噪声强度的增加, 当系统出现相干共振时, 如果给系统外加一个弱周期驱动力, 几乎在同一时刻, 系统也出现了随机共振现象; 但随着乘性噪声强度的增加, 仅当加性噪声和乘性噪声之间相关时, 此结论成立. 并且系统参数对相干共振和随机共振的影响是一致的. 关键词： 双稳态系统 随机共振 相干共振     

Coherence resonance in globally coupled neuronal networks with different neuron numbers

Because a brain consists of tremendous neuronal networks with different neuron numbers ranging from tens to tens of thousands, we study the coherence resonance due to ion channel noises in globally coupled neuronal networks with different neuron numbers. We confirm that for all neuronal networks with different neuron numbers there exist the array enhanced coherence resonance and the optimal synaptic conductance to cause the maximal spiking coherence. Furthermoremore, the enhancement effects of coupling on spiking coherence and on optimal synaptic conductance are almost the same, regardless of the neuron numbers in the neuronal networks. Therefore for all the neuronal networks with different neuron numbers in the brain, relative weak synaptic conductance (0.1 mS/cm²) is sufficient to induce the maximal spiking coherence and the best sub-threshold signal encoding.     

非线性动力系统分岔点邻域内随机共振的特性

研究了叉形分岔系统和FitzHugh Nagumo(FHN)细胞模型两种非线性动力系统分岔点邻域内 随机共振的特性.研究结果表明：这两种系统在分岔发生时具有由一个吸引子变为两个吸引 子或者由两个吸引子变为一个吸引子共同的分岔特性，即在分岔点的邻域内, 系统在分岔点 的两侧有分岔前吸引子和分岔后吸引子存在，在噪声的作用下，系统的运动除了像传统随机 共振的机理那样在分岔点一侧共存的吸引子之间跃迁，还在分岔点两侧三个吸引子（分岔前 一个吸引子和分岔后两个吸引子）之间跃迁，并且这种跃迁单独诱发了随机共振 ；在两种 跃迁都发生的情况下, 在其分岔点的邻域内，由第二种跃迁诱发的随机共振在引起第一种跃 迁噪声的强度很大的范围内变化仍可维持, 而第一种跃迁诱发的随机共振在引起第二种跃迁 噪声的强度很小的范围内变化即迅速消失. 关键词： 随机共振 吸引子 分岔点 跃迁     

Erratum to "Coherence resonance in globally coupled neuronal networks with different neuron numbers"

正The expression of Eq. (1) in page 028702-2 of Ref. [1] is inaccurate. This correct formula should be CmdVi/dt = gNam3ihi(Vi-VNa)     

Stochastic resonance in hybrid scale-free neuronal networks

We study the phenomenon of stochastic resonance in a system of coupled neurons that are globally excited by a weak periodic input signal. We make the realistic assumption that the chemical and electrical synapses interact in the same neuronal network, hence constituting a hybrid network. By considering a hybrid coupling scheme embedded in the scale-free topology, we show that the electrical synapses are more efficient than chemical synapses in promoting the best correlation between the weak input signal and the response of the system. We also demonstrate that the average degree of neurons within the hybrid scale-free network significantly influences the optimal amount of noise for the occurrence of stochastic resonance, indicating that there also exists an optimal topology for the amplification of the response to the weak input signal. Lastly, we verify that the presented results are robust to variations of the system size.     

一类非线性神经网络系统的超阈值随机共振现象

超阈值随机共振可用来解释一些生物现象.本文对一类非线性多阈值神经网络模型的超阈值 随机共振现象进行了探讨. 首先推导出了系统输出互信息的表达式, 然后分析了系统参数及噪声对互信息量的影响.通过数值计算发现,在阈值系统的信息传递过程中, 根据乘性噪声和加性噪声对系统信息传递影响的不同, 对系统的阈值进行恰当选取是至关重要的. 此外, 还发现系统的阈值单元数目越多, 超阈值随机共振现象就越容易出现.     

一类五次方振子系统的叉形分叉及振动共振研究

研究了一类具有分数阶导数阻尼的五次方振子系统中的叉形分叉及振动共振现象. 基于快慢变量分离法, 消去系统中的高频激励成分, 得到关于慢变量的等效系统, 根据等效系统中稳态平衡点的变化情况研究了系统的叉形分叉现象. 结果表明: 高频信号幅值的递增变化会引起亚临界叉形分叉, 高频信号频率和分数阶导数阻尼阶数的递增变化都会引起超临界叉形分叉; 振动共振和叉形分叉是关联的, 当叉形分叉发生时, 振动共振曲线会出现两个峰值, 否则只会出现一个峰值. 通过解析结果和数值模拟结果的对比, 验证了解析分析的正确性. 关键词： 亚临界叉形分叉 超临界叉形分叉 分数阶导数阻尼 振动共振     

Measuring spatial coherence by using a mask with multiple apertures

A simple method to measure the complex degree of spatial coherence of a partially coherent quasi-monochromatic light field is presented. The Fourier spectrum of the far-field interferogram generated by a mask with multiple apertures (small circular holes) is analyzed in terms of classes of aperture pairs. A class of aperture pairs is defined as the set of aperture pairs with the same separation vector. The height of the peaks in the magnitude spectrum determines the modulus of the complex degree of spatial coherence and the corresponding value in the phase spectrum determines the phase of the complex degree of spatial coherence. The method is illustrated with experimental results.     

Observation of intermolecular double-quantum coherence signal dips in nuclear magnetic resonance

The correlated spectroscopy revamped by asymmetric Z-gradient echo detection (CRAZED) sequence is modified to investigate intermolecular double-quantum coherence nuclear magnetic resonance signal dips in highly polarized spin systems. It is found that the occurrence of intermolecular double-quantum coherence signal dips is related to sample geometry, field inhomogeneity and dipolar correlation distance. If the field inhomogeneity is refocused, the signal dip occurs at a fixed position whenever the dipolar correlation distance approaches the sample dimension. However, the position is shifted when the field inhomogeneity exists. Experiments and simulations are performed to validate our theoretic analysis. These signal features may offer a unique way to investigate porous structures and may find applications in biomedicine and material science.     

小世界生物神经网络的相干共振研究

研究了无外界周期信号时Hodgkin-Huxley模型小世界生物神经网络的非线性响应.数值模拟结果显示：当噪声强度取某一有限值时,峰序列有序度可以达到最大,即产生相干共振现象.同时发现： 随着网络规模N的变化,相干共振系数cv的极小值不是一个,而是多个.这表明相干共振可发生在神经元集群数目特定的不同规模的网络中. 关键词： 相干共振 有序度 小世界网络 生物神经网络     

生物钟基因网络中分子噪声诱导的日夜节律振荡及相干共振

研究了果蝇细胞内生物钟基因调节网络的分子噪声，特别讨论了生物钟系统处于略微远离振荡区域的稳态时分子噪声对于时钟蛋白的日夜节律振荡的影响.结果表明：(1)虽然时钟蛋白合成或者衰减的生化反应事件是在随机的时间间隔里随机发生的，但系统可以依赖自身固有的调节机理诱导出明显的日夜节律振荡；(2)分子噪声诱导的日夜节律振荡的相干性可以在合适的分子噪声水平下到达最佳，说明了相干共振现象的发生.     

生物钟基因网络中分子噪声诱导的日夜节律振荡及相干共振

研究了果蝇细胞内生物钟基因调节网络的分子噪声,特别讨论了生物钟系统处于略微远离振荡区域的稳态时分子噪声对于时钟蛋白的日夜节律振荡的影响.结果表明：(1)虽然时钟蛋白合成或者衰减的生化反应事件是在随机的时间间隔里随机发生的,但系统可以依赖自身固有的调节机理诱导出明显的日夜节律振荡;(2)分子噪声诱导的日夜节律振荡的相干性可以在合适的分子噪声水平下到达最佳,说明了相干共振现象的发生. 关键词： 生物钟 分子噪声 日夜节律振荡 相干共振     

小世界神经网络的二次超谐波随机共振

随机共振现象是非线性系统中普遍存在的自然现象.主要通过研究小世界生物神经网络中的输出信噪比与反映小世界效应的重连概率p、耦合强度c以及输入信号振幅A之间的关系，来揭示小世界生物神经网络的二次超谐波随机共振的一些规律.发现对于Hodgkin-Huxley小世界神经网络，并不是信号越强，信噪比越大，而是输入信号的振幅A存在一个最优值A_O，此时网络信噪比最大.     

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.     

Spatiotemporal multiple coherence resonances and calcium waves in a coupled hepatocyte system

Spatiotemporal multiple coherence resonances for calcium activities induced by weak Gaussian white noise in coupled hepatocytes are studied. It is shown that bi-resonances in hepatocytes are induced by the interplay and competition between noise and coupling of cells, in other words, the cell in network can be excited either by noise or by its neighbour via gap junction which can transfer calcium ions between cells. Furthermore, the intercellular annular calcium waves induced by noise are observed, in which the wave length decreases with noise intensity augmenting but increases monotonically with coupling strength increasing. And for a fixed noise level, there is an optimal coupling strength that makes the coherence resonance reach maximum.