Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons

Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin-Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining the impact of diffusive and small-world network topology that determines the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.     

Channel noise-induced temporal coherence transitions and synchronization transitions in adaptive neuronal networks with time delay

Using spike-timing-dependent plasticity (STDP), we study the effect of channel noise on temporal coherence and synchronization of adaptive scale-free Hodgkin-Huxley neuronal networks with time delay. It is found that the spiking regularity and spatial synchronization of the neurons intermittently increase and decrease as channel noise intensity is varied, exhibiting transitions of temporal coherence and synchronization. Moreover, this phenomenon depends on time delay, STDP, and network average degree. As time delay increases, the phenomenon is weakened, however, there are optimal STDP and network average degree by which the phenomenon becomes strongest. These results show that channel noise can intermittently enhance the temporal coherence and synchronization of the delayed adaptive neuronal networks. These findings provide a new insight into channel noise for the information processing and transmission in neural systems.     

Multiple Spatial Coherence Resonances and Spatial Patterns in a Noise-Driven Heterogeneous Neuronal Network

Heterogeneity of the neurons and noise are inevitable in the real neuronal network. In this paper, Gaussian white noise induced spatial patterns including spiral waves and multiple spatial coherence resonances are studied in a network composed of Morris-Lecar neurons with heterogeneity characterized by parameter diversity. The relationship between the resonances and the transitions between ordered spiral waves and disordered spatial patterns are achieved. When parameter diversity is introduced, the maxima of multiple resonances increases first, and then decreases as diversity strength increases, which implies that the coherence degrees induced by noise are enhanced at an intermediate diversity strength. The synchronization degree of spatial patterns including ordered spiral waves and disordered patterns is identified to be a very low level. The results suggest that the nervous system can profit from both heterogeneity and noise, and the multiple spatial coherence resonances are achieved via the emergency of spiral waves instead of synchronization patterns.     

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.     

Parameter Diversity Induced Multiple Spatial Coherence Resonances and Spiral Waves in Neuronal Network with and Without Noise

Diversity in the neurons and noise are inevitable in the real neuronal network. In this paper, parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise are simulated. The relationship between the multiple resonances and the multiple transitions between patterns of spiral waves are identified. The coherence degrees induced by the diversity are suppressed when noise is introduced and noise density is increased. The results suggest that natural nervous system might profit from both parameter diversity and noise, provided a possible approach to control formation and transition of spiral wave by the cooperation between the diversity and noise.     

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.     

Role of the driving frequency in a randomly perturbed Hodgkin-Huxley neuron with suprathreshold forcing

The present paper examines the influence of the forcing frequency on the response of a randomly perturbed Hodgkin-Huxley system in the realm of suprathreshold amplitudes. Our results show that, in the presence of noise, the choice of driving frequency can seriously affect the precision of the external information transmission. At the same level of noise the precision can either decrease or increase depending on the driving frequency. We demonstrate that the destructive influence of noise on the interspike interval can be effectively reduced. That is, with driving signals in certain frequency ranges, the system can show stable periodic spiking even for relatively large noise intensities. Here, the most accurate transmission of an external signal occurs. Outside these frequency ranges, noise of the same intensity destroys the regularity of the spike trains by suppressing the generation of some spikes. On the other hand, we show that noise can have a reconstructive role for certain driving frequencies. Here, increasing noise intensity enhances the coherence of the neuronal response.     

Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.     

Multiple spatial coherence resonance induced by the stochastic signal in neuronal networks near a saddle-node bifurcation

This paper reported multiple induction of spiral waves with a stochastic signal in a square lattice network model composed of type I Morris-Lecar (ML) neurons, where each neuron is coupled to its four nearest neighbors. The induction occurs in two or three distinct regions of noise intensity, and thus enables emergence of multiple spatial coherence in the network, demonstrating a novel evidence of multiple coherence resonance. Emergence of this multiple spatial coherence resonance was evidenced by calculating the degree of spatial complexity, spatial correlation length, spatial structure function, circular symmetry, and signal-to-noise ratio curves. The network was further characterized by spatial frequency and inherent spatial scale, reflecting its inherent ability to manifest ordered pattern formation under the driven of noisy signals.     

Pacemaker-guided noise-induced spatial periodicity in excitable media

We study the impact of subthreshold periodic pacemaker activity and internal noise on the spatial dynamics of excitable media. For this purpose, we examine two systems that both consist of diffusively coupled units. In the first case, the local dynamics of the units is driven by a simple one-dimensional model of excitability with a piece-wise linear potential. In the second case, a more realistic biological system is studied, and the local dynamics is driven by a model for calcium oscillations. Internal noise is introduced via the τ-leap stochastic integration procedure and its intensity is determined by the finite size of each constitutive system unit. We show that there exists an intermediate level of internal stochasticity for which the localized pacemaker activity maps best into coherent periodic waves, whose spatial frequency is uniquely determined by the local subthreshold forcing. Via an analytical treatment of the simple minimal model for the excitable spatially extended system, we explicitly link the pacemaker activity with the spatial dynamics and determine necessary conditions that warrant the observation of the phenomenon in excitable media. Our results could prove useful for the understanding of interplay between local and global agonists affecting the functioning of tissue and organs.     

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.     

Pattern Synchronization in a Two-Layer Neuronal Network

Pattern synchronization in a two-layer neuronal network is studied. For a single-layer network of Rulkov map neurons, there are three kinds of patterns induced by noise. Additive noise can induce ordered patterns at some intermediate noise intensities in a resonant way; however, for small and large noise intensities there exist excitable patterns and disordered patterns, respectively. For a neuronal network coupled by two single-layer networks with noise intensity differences between layers, we find that the two-layer network can achieve synchrony as the interlayer coupling strength increases. The synchronous states strongly depend on the interlayer coupling strength and the noise intensity difference between layers.     

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.     

Breakup of Spiral Waves in Coupled Hindmarsh--Rose Neurons

Breakup of spiral wave in the Hindmarsh-Rose neurons with nearest-neighbour couplings is reported. Appropriate initial values and parameter regions are selected to develop a stable spiral wave and then the Gaussian coloured noise with different intensities and correlation times is imposed on all neurons to study the breakup of spiral wave, respectively. Based on the mean field theory, the statistical factor of synchronization is defined to analyse the evolution of spiral wave. It is found that the stable rotating spiral wave encounters breakup with increasing intensity of Gaussian coloured noise or decreasing correlation time to certain threshold.     

Detection of Mechanism of Noise-Induced Synchronization between Two Identical Uncoupled Neurons

We investigate the noise-induced synchronization between two identical uncoupled Hodgkin-Huxley neurons with sinusoidal stimulations. The numerical results confirm that the value of critical noise intensity for synchronizing two systems is much less than the magnitude of mean size of the attractor in the original system, and the deterministic feature of the attractor in the original system remains unchanged. This finding is significantly different from the previous work [Phys. Rev. E 67 （2003） 027201] in which the value of the critical noise intensity for synchronizing two systems was found to be roughly equal to the magnitude of mean size of the attractor in the original system, and at this intensity, the noise swamps the qualitative structure of the attractor in the original deterministic systems to synchronize to their stochastic dynamics. Further investigation shows that the critical noise intensity for synchronizing two neurons induced by noise may be related to the structure of interspike intervals of the original systems.     

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.     

Correlated noise induced spatiotemporal coherence resonance in a square lattice network

The effects of additive correlated noise, which is composed of common Gaussian white noise and local Gaussian colored noise, on a square lattice network locally modelled by the Rulkov map are studied. We focus on the ability of noise to induce pattern formation in a resonant manner. It is shown that local Gaussian colored noise is able to induce pattern formation, which is more coherent at some noise intensity or correlation time, so it is able to induce spatiotemporal coherence resonance in the network. When common Gaussian white noise is applied in addition, it is seen that the correlated noise can induce coherent spatial structures at some intermediate noise correlation, while this is not the case for smaller and larger noise intensities. The mechanism of the observed spatiotemporal coherence resonance is discussed. It is also found that the correlation time of local colored noise has no evident effect on the optimal value of the noise strength for spatiotemporal coherence resonance in the network.     

Control coherence resonance by noise recycling

We study the effect of recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay, in a parameter region below the threshold of supercritical Hopf bifurcation, by focussing on the performance of noise induced oscillations and coherence resonance. For fixed noise intensity, the amplitude and signal-to-noise ratio of the oscillation show periodic dependences on the delay time. The optimal noise intensity for the occurrence of coherence resonance also shows a periodic dependence on the delay. A theoretical analysis based on the stochastic normal form theory is presented, which qualitatively reproduces the simulation results with good agreement. This work presents a possible strategy for controlling noise induced oscillations and coherence resonance by deliberately adjusting the parameters of the recycled noise.     

Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise

We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the recovery variable is subject to noise. We investigate the role of the colored noise on the neuron dynamics by the mean response time (MRT) of the neuron. We find meaningful modifications of the resonant activation (RA) and noise enhanced stability (NES) phenomena due to the correlation time of the noise. For strongly correlated noise we observe suppression of NES effect and persistence of RA phenomenon, with an efficiency enhancement of the neuronal response. Finally we show that the self-correlation of the colored noise causes a reduction of the effective noise intensity, which appears as a rescaling of the fluctuations affecting the FHN system.     

钠离子和钾离子通道噪声扰动对神经网络 时空模式的影响

研究了钠离子和钾离子通道噪声扰动对Hodgkin-Huxley神经网络放电时空模式的影响. 发现无论钠离子通道噪声还是钾离子通道噪声扰动, 当取定一组温度、噪声强度, 随着耦合强度的增大, 神经网络放电时空斑图总能演化出螺旋波, 而且存在形成螺旋波所需的临界耦合强度. 分析发现钠离子通道噪声有利于神经网络螺旋波的形成, 而钾离子通道噪声不利于螺旋波形成. 结果还表明较低的温度能够使神经网络对噪声更加敏感. 最后, 讨论了特定参数下螺旋波与靶波之间的转化现象.