神经网络时滞系统非共振双Hopf分岔及其广义同步

本文建立了具有自连接和抑制-兴奋型他连接的两个同性神经元模型。其中自连接是由于兴奋型的突触产生,而他连接则分别对应于两神经元兴奋、抑制型的突触。发现如果有兴奋型自连接就会有双Hopf分岔,而没有时滞自连接时双Hopf分岔就会消失,因此自连接引起了双Hopf分岔。作为一个例子,通过变动连接中的时滞和他连接中的比重,1／√2双Hopf分岔得到了详细研究。通过中心流形约化,分岔点邻域内各种不同的动力学行为得到了分类,并以解析形式表出。神经元活动的分岔路径得以表明。从得到的解析近似解可以发现,本文所研究的具有兴奋一抑制型他连接的两相同神经元的节律不能完全同步而只能广义同步。时滞也可以使其节律消失,两神经元变为非活动的。这些结果在控制神经网络关联记忆和设计人工神经网络方面有着潜在的应用。     

耦合条件下大脑皮层神经振子群的能量函数

探讨了局部脑皮层网络活动中,耦合条件下的大规模神经振子群的能量消耗与神经信号编码之间的内禀关系,得到了神经元集群在阈下和阈上互相耦合时神经元膜电位变化的函数. 这个能量函数能够精确地再现神经电生理学实验中的EPSP,IPSP,动作电位以及动作电流. 最近功能性核磁共振实验证明了神经信号的编码是与能量的消耗紧密地耦合在一起的,因此研究结果表明利用能量原理研究大脑在神经网络层次上是如何进行编码的这一重大科学问题的讨论是十分有益的. 可以预计得到的能量函数将是生物学神经网络动力学稳定性计算的基础.      

A feasible neuron for estimating the magnetic field effect

Biological neurons are capable of encoding a variety of stimuli, and the synaptic plasticity can be enhanced for activating appropriate firing modes in the neural activities. Artificial neural circuits are effective to reproduce the main biophysical properties of neurons when the nonlinear circuits composed of reliable electronic components with distinct physical properties are tamed to generate similar firing patterns as biological neurons. In this paper, a simple neural circuit is proposed to estimate the effect of magnetic field on the neural activities by incorporating two physical electronic components. A magnetic flux-controlled memristor and an ideal Josephson junction in parallel connection are used to percept the induction currents induced by the magnetic field. The circuit equations are obtained according to the Kirchhoff’s theorem and an equivalent neuron model is acquired by applying scale transformation on the physical variables and parameters in the neural circuit. Standard bifurcation analysis is calculated to predict possible mode transition and evolution of firing patterns. The Hamilton energy is also obtained to find its dependence on the mode selection in electronic activities. Furthermore, External magnetic field is applied to estimate the mode transition of neural activities because the phase error and the junction current across the Josephson junction can be adjusted to change the dynamics of the neural circuit. It is found that the biophysical functional neuron can present rapid and sensitive response to external magnetic field. Nonlinear resonance is obtained when stochastic phase error is induced by external time-varying magnetic field. The neural circuit can be suitable for further calculating the collective behaviors of neurons exposed to magnetic field.

     

A proposed hybrid neural network for position control of a walking robot

The use of a proposed recurrent neural network control system to control a four-legged walking robot is presented in this paper. The control system consists of a neural controller, a standard PD controller, and the walking robot. The robot is a planar four-legged walking robot. The proposed Neural Network (NN) is employed as an inverse controller of the robot. The NN has three layers, which are input, hybrid hidden and output layers. In addition to feedforward connections from the input layer to the hidden layer and from the hidden layer to the output layer, there is also a feedback connection from the output layer to the hidden layer and from the hidden layer to itself. The reason to use a hybrid layer is that the robot’s dynamics consists of linear and nonlinear parts. The results show that the neural-network controller can efficiently control the prescribed positions of the stance and swing legs during the double stance phase of the gait cycle after sufficient training periods. The goal of the use of this proposed neural network is to increase the robustness of the control of the dynamic walking gait of this robot in the case of external disturbances. Also, the PD controller alone and Computed Torque Method (CTM) control system are used to control the walking robot’s position for comparison.     

Effects of the electromagnetic radiation on cognitive performance: a model study

We constructed a two-layer network model to study the effect of electromagnetic radiation on the cognitive functions. The network model was used to simulate two cognitive tasks under the electromagnetic radiation: the visual-guided saccade task and the memory-guided saccade task. The performance of these tasks showed that the electromagnetic radiation could induce faster ramping up activities, higher level of persistent activities and shorter reaction time, but the basic functions of the network such as working memory and motor output did not impair. We found that the electromagnetic radiation have both excitatory effect and inhibitory effect on the neuronal activities of the network model, but the excitatory effect played a major role. Finally, we concluded an excitatory mechanism to explain the effects of the electromagnetic radiation on the cognitive performance.

     

Predicting cortical oscillations with bidirectional LSTM network: a simulation study

It has been stated that up-down-state (UDS) cortical oscillation levels between excitatory and inhibitory neurons play a fundamental role in brain network construction. Predicting the time series behaviors of neurons in periodic and chaotic regimes can help in improving diseases, higher-order human activities, and memory consolidation. Predicting the time series is usually done by machine learning methods. In paper, the deep bidirectional long short-term memory (DBLSTM) network is employed to predict the time evolution of regular, large-scale UDS oscillations produced by a previously developed neocortical network model. In noisy time-series prediction tasks, we compared the DBLSTM performance with two other variants of deep LSTM networks: standard LSTM, LSTM projected, and gated recurrent unit (GRU) cells. We also applied the classic seasonal autoregressive integrated moving average (SARIMA) time-series prediction method as an additional baseline. The results are justified through qualitative resemblance between the bifurcation diagrams of the actual and predicted outputs and quantitative error analyses of the network performance. The results of extensive simulations showed that the DBLSTM network provides accurate short and long-term predictions in both periodic and chaotic behavioral regimes and offers robust solutions in the presence of the corruption process.

     

A finite-time recurrent neural network for solving online time-varying Sylvester matrix equation based on a new evolution formula

Sylvester equation is widely used to study the stability of a nonlinear system in the control field. In this paper, a finite-time Zhang neural network (FTZNN) is proposed and applied to online solution of time-varying Sylvester equation. Differing from the conventional accelerating method, the design of the proposed FTZNN model is based on a new evolution formula, which is presented and studied to accelerate the convergence speed of a recurrent neural network. Compared with the original Zhang neural network (ZNN) for time-varying Sylvester equation, the FTZNN model can converge to the theoretical time-varying solution within finite time, instead of converging exponentially with time. Besides, we can obtain the upper bound of the finite convergence time for the FTZNN model in theory. Simulation results show that the proposed FTZNN model achieves the better performance as compared with the original ZNN model for solving online time-varying Sylvester equation.     

神经系统疾病与认知动力学(II): 神经振荡与认知动力学

大脑神经系统具有从慢到快多种不同的振荡节律, 这些节律振荡被认为参与了大脑多种功能的实现, 其中高频的伽马同步振荡被认为与大脑的认知功能最为相关. 本文阐述了生物学实验方面关于伽马振荡及其功能的研究进展, 并针对实验中伽马振荡的频率敏感依赖于外部刺激特征的现象, 综述了基于神经网络模型进行变频伽马振荡及其认知功能的动力学建模研究工作, 解释了视觉刺激调控的变频率伽马振荡动力学产生机理, 提出了基于同步抑制增强全局放电率对比度的神经认知机制. 研究成果有助于理解神经系统同步振荡的产生机理及其认知作用, 为大脑认知原理以及类脑智能的研究奠定基础.      

Robust synchronization of uncertain fractional-order chaotic systems with time-varying delay

This paper presents a new technique using a recurrent non-singleton type-2 sequential fuzzy neural network (RNT2SFNN) for synchronization of the fractional-order chaotic systems with time-varying delay and uncertain dynamics. The consequent parameters of the proposed RNT2SFNN are learned based on the Lyapunov–Krasovskii stability analysis. The proposed control method is used to synchronize two non-identical and identical fractional-order chaotic systems, with time-varying delay. Also, to demonstrate the performance of the proposed control method, in the other practical applications, the proposed controller is applied to synchronize the master–slave bilateral teleoperation problem with time-varying delay. Simulation results show that the proposed control scenario results in good performance in the presence of external disturbance, unknown functions in the dynamics of the system and also time-varying delay in the control signal and the dynamics of system. Finally, the effectiveness of proposed RNT2SFNN is verified by a nonlinear identification problem and its performance is compared with other well-known neural networks.     

Multilayer brain network combined with deep convolutional neural network for detecting major depressive disorder

As a global and grievous mental disease, major depressive disorder (MDD) has received much attention. Accurate detection of MDD via physiological signals represents an urgent research topic. Here, a frequency-dependent multilayer brain network, combined with deep convolutional neural network (CNN), is developed to detect the MDD. Multivariate pseudo Wigner distribution is firstly introduced to extract the time-frequency characteristics from the multi-channel EEG signals. Then multilayer brain network is constructed, with each layer corresponding to a specific frequency band. Such multilayer framework is in line with the nature of the workings of the brain, and can effectively characterize the brain state. Further, a multilayer deep CNN architecture is designed to study the brain network topology features, which is finally used to accurately detect MDD. The experimental results on a publicly available MDD dataset show that the proposed approach is able to detect MDD with state-of-the-art accuracy of 97.27%. Our approach, combining multilayer brain network and deep CNN, enriches the multivariate time series analysis theory and helps to better characterize and recognize the complex brain states.

     

Estimating the state of epidemics spreading with graph neural networks

When an epidemic spreads into a population, it is often impractical or impossible to continuously monitor all subjects involved. As an alternative, we propose using algorithmic solutions that can infer the state of the whole population from a limited number of measures. We analyze the capability of deep neural networks to solve this challenging task. We base our proposed architecture on Graph Convolutional Neural Networks. As such, it can reason on the effect of the underlying social network structure, which is recognized as the main component in spreading an epidemic. The proposed architecture can reconstruct the entire state with accuracy above 70%, as proven by two scenarios modeled on the CoVid-19 pandemic. The first is a generic homogeneous population, and the second is a toy model of the Boston metropolitan area. Note that no retraining of the architecture is necessary when changing the model.

     

Experimental study and artificial neural network modeling of unsteady laminar forced convection in a rectangular duct

In this study, an artificial neural network (ANNs) for the prediction of unsteady heat transfer in a rectangular duct was studied. The ANNs has been applied for the unsteady heat transfer in a rectangular duct. An experimental study has been carried out to investigate the axial variation of inlet temperature and the impact of inlet frequency on decay indices in the thermal entrance region of a parallel plate channel. The investigation was conducted with laminar forced flows for Reynolds numbers ranging from 1,120 to 2,200 while the inlet heat input frequency varied from 0.02 to 0.24 Hz. The results revealed that the ANNs can be used for modeling unsteady heat transfer in the duct. The accuracy between experimental and ANNs approach results was achieved with a mean absolute relative error less than 39%.     

On hyperchaos in a small memristive neural network

This paper studies a small Hopfield neural network with a memristive synaptic weight. We show that the previous stable network after one weight replaced by a memristor can exhibit rich complex dynamics, such as quasi-periodic orbits, chaos, and hyperchaos, which suggests that the memristor is crucial to the behaviors of neural networks and may play a significant role. We also prove the existence of a saddle periodic orbit, and then present computer-assisted verification of hyperchaos through a homoclinic intersection of the stable and unstable manifolds, which gives a positive answer to an interesting question that whether a 4D memristive system with a line of equilibria can demonstrate hyperchaos.     

Three-dimensional microscopic interlaminar analysis of cross-ply laminates based on a homogenization theory

In this study, a method for three-dimensional microscopic interlaminar analysis of cross-ply laminates is developed based on a homogenization theory to analyze microscopic interactions between unidirectional long fiber-reinforced laminae. For this, a unit cell of a cross-ply laminate, which includes interlaminar areas, is defined under the assumption that each lamina in the laminate has a transversely square fiber array. Then, showing that the laminate has a point-symmetric internal structure, the symmetry is utilized to introduce half of the unit cell as the domain of analysis. Moreover, the domain of analysis is divided into substructures using a substructure method combined with the homogenization theory, significantly reducing the computational costs. The present method is then applied to the analysis of interlaminar stress distributions in a carbon fiber/epoxy cross-ply laminate subjected to in-plane uniaxial tension. It is shown that microscopic shear stress noticeably occurs at the interface between the 0°- and 90°-plies. It is also shown that the microscopic interaction between the two plies is observed only in the vicinity of the interface.     

Synchronous firing patterns of neuronal population with excitatory and inhibitory connections

A stochastic model of neuronal population with excitatory and inhibitory connections is proposed, where excitatory synaptic dynamics is considered. Oscillatory synchronized firing patterns of a neuronal population by means of firing density are investigated. Numerical simulations using Fokker-Planck equation show that slow inhibitory connection contributes to oscillatory synchronized firing of the neuronal population, and synchronous activity is enhanced due to inhibitory connection. The effect of time delay on the oscillatory synchronized firing in the neuronal population using phase mode is explored. Numerical simulation indicates that short synaptic transmission delay can suppress oscillatory synchronized firing, but this suppression is instable.     

Solving time-varying inverse kinematics problem of wheeled mobile manipulators using Zhang neural network with exponential convergence

A mobile manipulator is a robotic device composed of a mobile platform and a stationary manipulator fixed to the platform. The forward kinematics problem for such mobile manipulators has a mathematical analytic solution; however, the inverse kinematics problem is mathematically intractable (especially for satisfying real-time requirements). To obtain the accurate solution of the time-varying inverse kinematics for mobile manipulators, a special class of recurrent neural network, named Zhang neural network (ZNN), is exploited and investigated in this article. It is theoretically proven that such a ZNN model globally and exponentially converges to the solution of the time-varying inverse kinematics for mobile manipulators. In addition, the kinematics equations of the mobile platform and the manipulator are integrated into one system, and thus the resultant solution can co-ordinate simultaneously the wheels and the manipulator to fulfill the end-effector task. For comparison purposes, a gradient neural network (GNN) is developed for solving time-varying inverse kinematics problem of wheeled mobile manipulators. Finally, we conduct extensive tracking-path simulations performed on a wheeled mobile manipulator using such a ZNN model. The results substantiate the efficacy and high accuracy of the ZNN model for solving time-varying inverse kinematics problem of mobile manipulators. Besides, by comparing the simulation results of the GNN and ZNN models, the superiority of the ZNN model is demonstrated clearly.     

大脑血液动力学现象中的能量编码

神经信息的编码与解码是神经科学中的核心研究内容,同时又极具挑战性.传统的编码理论都具有各自的局限性,很难从脑的全局运行方式上给出有效的理论.而由于能量是一个标量具有可叠加性,因此能量编码理论可以从神经元活动的能量特征出发来研究脑功能的全局神经编码问题,取得了一系列的研究成果.本研究以王-张神经元能量计算模型为基础,构建了一个多层次结构的神经网络,通过计算机数值模拟得到了神经网络的能量消耗和血液中葡萄糖供能的变化情况.计算结果显示,和网络的神经活动达到峰值的时间相比,血液中葡萄糖的供能达到峰值的时间延迟了约5.6s.从定量的角度再现了功能性核磁共振(fMRI)中的血液动力学现象:大脑某个脑区的神经元集群被激活以后经过5~7 s的延迟,脑血流的变化才会大幅增加.模拟结果表明先前发表的由王-张神经元模型所揭示的负能量机制在控制大脑的血液动力学现象中起着核心的作用,预测了刺激条件下大脑的能量代谢与血流之间变化的本质是由神经元在发放动作电位过程中正、负能量之间的非平衡、不匹配性质所决定的.本文的研究结果为今后进一步探究血液动力学现象的生理学机制提供了新的研究方向,在神经网络的建模与计算方面给出了一个新的视角和研究方法.      

Sampled-data state estimation for delayed neural networks with Markovian jumping parameters

This paper is concerned with the sampled-data state estimation problem for a class of delayed neural networks with Markovian jumping parameters. Unlike the classical state estimation problem, in our state estimation scheme, the sampled measurements are adopted to estimate the concerned neuron states. The neural network under consideration is assumed to have multiple modes that switch from one to another according to a given Markovian chain. By utilizing the input delay approach, the sampling period is converted into a time-varying yet bounded delay. Then a sufficient condition is given under which the resulting error dynamics of the neural networks is exponentially stable in the mean square. Based on that, a set of sampled-data estimators is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using the available software. Finally, a numerical example is used to show the effectiveness of the estimation approach proposed in this paper.     

Dynamical response,information transition and energy dependence in a neuron model driven by autapse

Autapses are a class of special synapses of neurons. In those neurons, their axons are not connected to the dendrites of other neurons but are attached to their own cell bodies. The output signal of a neuron feeds back to itself, thereby allowing the neuronal firing behavior to be self-tuned. Autapses can adjust the firing accuracy of a neuron and regulate the synchronization of a neuronal system. In this paper, we investigated the information capacity and energy efficiency of a Hodgkin–Huxley neuron in the noisy signal transmission process regulated by delayed inhibitory chemical autapse for different feedback strengths and delay times. We found that the information transmission, coding efficiency, and energy efficiency are maximized when the delay time is half of the input signal period. With the increase in the inhibitory strength of autapse, this maximization is increasingly obvious. Therefore, we propose that the inhibitory autaptic structure can serve as a mechanism and enable neural information processing to be energy efficient.

     

Evoking complex neuronal networks by stimulating a single neuron

The responses of electrically coupled neuronal network to external stimulus injected on a single neuron are investigated. Stimulating the largest-degree neuron in the network, it is found that as the intensity of the stimulus increases, the network will be transiting from the resting to firing states and then restoring to the resting state, thereby showing a bounded firing region in the parameter space. Furthermore, it is found that as the coupling strength among the neurons decreases, the firing region is gradually expanded and, at the weak couplings, it could be separated into several disconnected subregions. By a simplified network model, we conduct a detailed analysis on the bifurcation diagram of the network dynamics in the two-dimensional parameter space spanned by stimulating intensity and coupling strength, and, by introducing a new coefficient named effective stimulus, explore the underlying mechanisms for the modified firing region. It is revealed that the coupling strength and stimulating intensity are equally important in evoking the network, but with different mechanisms. Specifically, the effective stimuli are shifted up globally by increasing the stimulating intensity, while are drawn closer by increasing the coupling strength. The dynamical responses of small-world and random complex networks to external stimulus are also investigated, which confirm the generality of the observed phenomena. The findings shed new lights on the collective behaviors of complex neuronal networks and might help our understandings on the recent experimental results.