Stochastic resonance on a modular neuronal network of small-world subnetworks with a subthreshold pacemaker

We study the phenomenon of stochastic resonance on a modular neuronal network consisting of several small-world subnetworks with a subthreshold periodic pacemaker. Numerical results show that the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the intensity of additive spatiotemporal noise. This effect of pacemaker-driven stochastic resonance of the system depends extensively on the local and the global network structure, such as the intra- and inter-coupling strengths, rewiring probability of individual small-world subnetwork, the number of links between different subnetworks, and the number of subnetworks. All these parameters play a key role in determining the ability of the network to enhance the noise-induced outreach of the localized subthreshold pacemaker, and only they bounded to a rather sharp interval of values warrant the emergence of the pronounced stochastic resonance phenomenon. Considering the rather important role of pacemakers in real-life, the presented results could have important implications for many biological processes that rely on an effective pacemaker for their proper functioning.     

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.     

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.     

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.     

二维格子神经元网络的振动共振和非线性振动共振

本文采用数值模拟的方法, 在通过电突触耦合或化学突触耦合的二维格子神经元网络中, 研究了FitzHugh-Nagumo神经元受到双频信号输入时神经元网络对低频信号的响应特性. 结果表明:当固定受到双频输入信号的神经元在体系中所占的比例且FitzHugh-Nagumo神经元参数处于可激发区域时双频信号中的高频部分可诱导出动作电位产生, 而且随着高频输入信号强度的增加, 神经元网络对低频输入信号响应先增大后减小, 出现了极大值, 即发生了振动共振现象. 另外本文还研究了神经元网络对低频输入信号的二次谐波的响应, 同样发现了非线性振动共振现象, 并且体系对低频信号的响应随着其频率ω 的增加也产生共振现象, 即发生了双共振现象. 上述共振现象在以电突触耦合的二维格子神经元网络中和以化学突触耦合的二维格子神经元网络中都可以观察到. 当固定双频输入信号中高频输入信号强度时, 随着受到双频输入信号的神经元在体系中所占比例的变化, 电突触耦合的二维格子神经元网络对低频输入信号的响应与化学突触耦合的二维格子神经元网络对低频输入信号的响应相比有很大的不同.     

耦合小世界神经网络的随机共振

噪声广泛存在于生物神经系统中,对系统功能具有重要作用.采用神经元二维映射模型构建一个复杂神经网络,由多个小世界子网络构成,研究了Gaussian白噪声诱导的随机共振现象.研究发现,只有合适的噪声强度才能使神经网络对输入刺激信号的频率响应达到峰值.另外,网络结构对系统随机共振特性有重要影响.在固定的耦合强度下,存在一个最优的局部小世界子网络结构,使得整个系统的频率响应最佳.     

线性时滞反馈引起的周期性振动共振分析

研究了高频信号和微弱低频信号同时激励下线性时滞反馈对过阻尼双稳系统和Duffing振子系统中振动共振现象的影响. 解析分析和数值结果都表明, 系统对低频信号的响应幅值增益随时滞参数的变化同时呈现两种不同的周期性关系, 其周期分别为输入的高频信号和低频信号的周期. 数值结果还表明, 对不存在经典振动共振现象的单稳Duffing系统, 通过调节时滞参数也可以引发振动共振现象. 使用时滞反馈不仅可以有效地控制振动共振, 还可以进一步增强系统对微弱低频信号的响应. 关键词： 双稳系统 Duffing 系统 线性时滞反馈 振动共振     

具有时滞反馈的非对称双稳系统中的振动共振研究

研究了具有时滞反馈的非对称双稳系统中的振动共振现象. 在绝热近似条件下, 应用快慢变量分离法得到系统响应振幅的解析表达式Q, 分析了时滞参数α和不对称参数r对振动共振现象的影响. 结果表明: 在Q-α平台上, α可以诱导响应幅值的极大值以输入高频信号和低频信号的周期出现. 不对称参数并不影响共振发生的位置, 但是能够增强响应幅值. 在Q-B (B为高频信号振幅)平台上, 共振发生的位置B_VR随着α呈现两种不同的周期关系, 且周期分别为输入高频信号和低频信号的周期. 在Q-Ω (Ω高频信号频率)平台上, 随着时滞参数的增大, 当B较小时, 在Ω的小值区间内, Q呈现出多重共振现象, 在Ω的大值区间, Q趋于定值.     

Analysis and time-delay synchronisation of chaotic satellite systems

The effect of depth and location of a triple-well potential on vibrational resonance is investigated in a quintic oscillator driven by a low-frequency force and a high-frequency force. The values of low-frequency \(\omega \) and amplitude g of the high-frequency force at which vibrational resonance occurs are derived both numerically and theoretically. It is found that: as \(\omega \) varies, at most one resonance takes place and the response amplitude at resonance depends on the depth and the location of the potential wells. When g is altered, the depth and location of wells can control the number of resonances, resulting in two, three and four resonances. The system parameters can be adjusted by controlling the depth and position of the wells to achieve optimum vibrational resonance. Furthermore, the changes induced by these two quantities in the tristable system are found to be richer than those induced in bistable systems.     

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     

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.     

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.     

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.     

Coevolution of information processing and topology in hierarchical adaptive random Boolean networks

Random Boolean Networks (RBNs) are frequently used for modeling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive random Boolean Network (HARBN) as a system consisting of distinct adaptive RBNs (ARBNs) – subnetworks – connected by a set of permanent interlinks. We investigate mean node information, mean edge information as well as mean node degree. Information measures and internal subnetworks topology of HARBN coevolve and reach steady-states that are specific for a given network structure. The main natural feature of ARBNs, i.e. their adaptability, is preserved in HARBNs and they evolve towards critical configurations which is documented by power law distributions of network attractor lengths. The mean information processed by a single node or a single link increases with the number of interlinks added to the system. The mean length of network attractors and the mean steady-state connectivity possess minima for certain specific values of the quotient between the density of interlinks and the density of all links in networks. It means that the modular network displays extremal values of its observables when subnetworks are connected with a density a few times lower than a mean density of all links.     

A modular attachment mechanism for software network evolution

A modular attachment mechanism of software network evolution is presented in this paper. Compared with the previous models, our treatment of object-oriented software system as a network of modularity is inherently more realistic. To acquire incoming and outgoing links in directed networks when new nodes attach to the existing network, a new definition of asymmetric probabilities is given. Based on this, modular attachment instead of single node attachment in the previous models is then adopted. The proposed mechanism is demonstrated to be able to generate networks with features of power-law, small-world, and modularity, which represents more realistic properties of actual software networks. This work therefore contributes to a more accurate understanding of the evolutionary mechanism of software systems. What is more, explorations of the effects of various software development principles on the structure of software systems have been carried out, which are expected to be beneficial to the software engineering practices.     

Controlling vibrational resonance in a multistable system by time delay

The phenomenon of vibrational resonance in a delayed multistable system that is excited by biharmonic signals is investigated in the present paper. Different from the former theory, the appearance and the disappearance of the vibrational resonance are controlled by adjusting the time delay parameter instead of modulating the amplitude of the high-frequency signal. The motion of the orbit within or between the different potential wells can also be controlled. Furthermore, based on both the methods of numerical simulation and analytical analysis, the behavior of delay-induced multiple vibrational resonance and its mechanism are investigated and discussed. The multiple vibrational resonance, which is quantified by the response amplitude at the low-frequency, is found to be periodic in the delay parameter with two periods, i.e., the periods of the two driven signals. The method used in this paper gives a new way for controlling vibrational resonance in a multistable system.     

Comparison of co-occurrence networks of the Chinese and English languages

Co-occurrence networks of Chinese characters and words, and of English words, are constructed from collections of Chinese and English articles, respectively. Four types of collections are considered, namely, essays, novels, popular science articles, and news reports. Statistical parameters of the networks are studied, including diameter, average degree, degree distribution, clustering coefficient, average shortest path length, as well as the number of connected subnetworks. It is found that the character and word networks of each type of article in the Chinese language, and the word network of each type of article in the English language all exhibit scale-free and small-world features. The statistical parameters of these co-occurrence networks are compared within the same language and across the two languages. This study reveals some commonalities and differences between Chinese and English languages, and among the four types of articles in each language from a complex network perspective. In particular, it is shown that expressions in English are briefer than those in Chinese in a certain sense.     

Investigating the topology of interacting networks

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere’s three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere’s vertical stratification and general circulation. Specifically, the new measure “cross-betweenness” identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective.     

Monomer-dimer model on a scale-free small-world network

The explicit determination of the number of monomer-dimer arrangements on a network is a theoretical challenge, and exact solutions to monomer-dimer problem are available only for few limiting graphs with a single monomer on the boundary, e.g., rectangular lattice and quartic lattice; however, analytical research (even numerical result) for monomer-dimer problem on scale-free small-world networks is still missing despite the fact that a vast variety of real systems display simultaneously scale-free and small-world structures. In this paper, we address the monomer-dimer problem defined on a scale-free small-world network and obtain the exact formula for the number of all possible monomer-dimer arrangements on the network, based on which we also determine the asymptotic growth constant of the number of monomer-dimer arrangements in the network. We show that the obtained asymptotic growth constant is much less than its counterparts corresponding to two-dimensional lattice and Sierpinski fractal having the same average degree as the studied network, which indicates from another aspect that scale-free networks have a fundamentally distinct architecture as opposed to regular lattices and fractals without power-law behavior.     

Stochastic resonance on paced genetic regulatory small-world networks: effects of asymmetric potentials

We study the phenomenon of stochastic resonance on small-world networks consisting of bistable genetic regulatory units, whereby the external subthreshold periodic forcing is introduced as a pacemaker trying to impose its rhythm on the whole network through the single unit to which it is introduced. Without the addition of additive spatiotemporal noise, however, the whole network remains forever trapped in one of the two stable steady states of the local dynamics. We show that the correlation between the frequency of subthreshold pacemaker activity and the response of the network is resonantly dependent on the intensity of additive noise. The reported pacemaker driven stochastic resonance depends significantly on the asymmetry of the two potential wells characterizing the bistable dynamics, which can be tuned via a single system parameter. In particular, we show that the ratio between the clustering coefficient and the characteristic path length is a suitable quantity defining the ability of a small-world network to facilitate the outreach of the pacemaker-emitted subthreshold rhythm, but only if the asymmetry between the potentials is practically negligible. In case of substantially asymmetric potentials the impact of the small-world topology is less profound and cannot warrant an enhancement of stochastic resonance by units that are located far from the pacemaker.