基于信息编码的神经能量计算

通过神经元活动期间神经能量的计算, 发现关于神经元 的活动需要消耗能量的观点并不完整. 计算表明神经元在动作电位发放期间先吸收 能量然后再消耗能量. 依据这个重要发现, 能够解释当脑内神经元被激活时脑血流 量大幅增加而耗氧量却增加很少这一难以解释的神经生理学现象. 同时还能够解释外部刺激信息和知觉的产生会有同步效应这一认知神经科学界也难 以解释的现象.     

Effect of spatially correlated noise on stochastic synchronization in globally coupled FitzHugh-Nagumo neuron systems

The phenomenon of stochastic synchronization in globally coupled FitzHugh-Nagumo (FHN) neuron system subjected to spatially correlated Gaussian noise is investigated based on dynamical mean-field approximation (DMA) and direct simulation (DS). Results from DMA are in good quantitative or qualitative agreement with those from DS for weak noise intensity and larger system size. Whether the consisting single FHN neuron is staying at the resting state, subthreshold oscillatory regime, or the spiking state, our investigation shows that the synchronization ratio of the globally coupled system becomes higher as the noise correlation coefficient increases, and thus we conclude that spatial correlation has an active effect on stochastic synchronization, and the neurons can achieve complete synchronization in the sense of statistics when the noise correlation coefficient tends to one. Our investigation also discloses that the noise spatial correlation plays the same beneficial role as the global coupling strength in enhancing stochastic synchronization in the ensemble. The result might be useful in understanding the information coding mechanism in neural systems.     

FitzHugh-Nagumo神经元网络的同步振荡与联想记忆

本文研究由FitzHugh—Nagumo神经元所组成的脉动神经元网络的同步与联想记忆恢复。基于神经元微观生理结构，本文给出具有空间随机分布延时的神经元间耦合，而这种随机分布延时描述了脉动信号从突触前神经元到突触后神经元在轴突上传播所需要的时间。记忆由空时发放的神经元集群表达，在噪声涨落的作用下，系统取得了对不完整输入的记忆恢复。     

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 review for dynamics in neuron and neuronal network

The biological Hodgkin–Huxley model and its simplified versions have confirmed its effectiveness for recognizing and understanding the electrical activities in neurons, and bifurcation analysis is often used to detect the mode transition in neuronal activities. Within the collective behaviors of neurons, neuronal network with different topology is designed to study the synchronization behavior and spatial pattern formation. In this review, the authors give careful comments for the presented neuron models and present some open problems in this field, nonlinear analysis could be effective to further discuss these problems and some results could be helpful to give possible guidance in the field of neurodynamics.     

MULTI-MODE OSCILLATIONS AND HAMILTON ENERGY FEEDBACK CONTROL OF A CLASS OF MEMRISTOR NEURON$^{\bf 1)}$

根据法拉第电磁感应定律,在离子穿越细胞膜或者在外界电磁辐射下,细胞内外的电生理环境会产生电磁感应效应,继而会影响神经元的电活动行为. 基于此,本文考虑电磁感应影响下的 Hindmarsh-Rose (HR) 神经元模型,研究了其混合模式振荡放电特征,并设计一个 Hamilton 能量反馈控制器,将其控制到不同的周期簇放电状态. 首先,通过理论分析发现磁通 HR 神经元系统的 Hopf 分岔使其平衡点的稳定性发生了改变,并产生极限环,进而研究了 Hopf 分岔点附近膜电压的放电特征. 基于双参数数值仿真发现该系统具有丰富的分岔结构,在不同的参数平面上存在倍周期分岔、伴有混沌的加周期分岔、无混沌的加周期分岔以及共存的混合模式振荡. 最后,为了有效控制膜电压的混合模式振荡,利用亥姆霍兹理论计算出磁通 HR 神经元系统的 Hamilton 能量函数并设计 Hamilton 能量反馈控制器,通过数值仿真分析了膜电压在不同反馈增益下的簇放电状态,发现该控制器能够有效地控制膜电压到不同的周期簇放电模式. 本文的研究结果为探究电磁感应下神经元的分岔结构及其能量控制领域提供了有用的理论支撑.     

一类忆阻神经元的电活动多模振荡及Hamilton 能量反馈控制

根据法拉第电磁感应定律,在离子穿越细胞膜或者在外界电磁辐射下,细胞内外的电生理环境会产生电磁感应效应,继而会影响神经元的电活动行为. 基于此,本文考虑电磁感应影响下的 Hindmarsh-Rose (HR) 神经元模型,研究了其混合模式振荡放电特征,并设计一个 Hamilton 能量反馈控制器,将其控制到不同的周期簇放电状态. 首先,通过理论分析发现磁通 HR 神经元系统的 Hopf 分岔使其平衡点的稳定性发生了改变,并产生极限环,进而研究了 Hopf 分岔点附近膜电压的放电特征. 基于双参数数值仿真发现该系统具有丰富的分岔结构,在不同的参数平面上存在倍周期分岔、伴有混沌的加周期分岔、无混沌的加周期分岔以及共存的混合模式振荡. 最后,为了有效控制膜电压的混合模式振荡,利用亥姆霍兹理论计算出磁通 HR 神经元系统的 Hamilton 能量函数并设计 Hamilton 能量反馈控制器,通过数值仿真分析了膜电压在不同反馈增益下的簇放电状态,发现该控制器能够有效地控制膜电压到不同的周期簇放电模式. 本文的研究结果为探究电磁感应下神经元的分岔结构及其能量控制领域提供了有用的理论支撑.      

Reproduce the biophysical function of chemical synapse by using a memristive synapse

Dynamical modeling of nervous systems is of fundamental importance in many scientific fields containing the topics relative to computational neuroscience and biophysics. Many feasible mathematical models have been suggested in the explanation and prediction of some features of neural activities. Considering the special experimental findings and the computational efficiency, it is necessary to find a perfect balance between estimating biophysical functions with complete dynamics and reducing complexity when a tractable model is built. In this paper, a chemical synaptic model is reproduced by using a memristive synapse because it not only remains synaptic characteristic but also exhibits a pinched hysteresis loop and active feature locally. That is, a neuron activated by chemical synapse can produce similar firing modes as the neuron coupled by a memristive synapse, and both the chemical synapse and memristive synapse have similar field effect and biophysical properties. By calculating the one-parameter and two-parameter bifurcation as well as the Lyapunov exponent spectrum, it is confirmed that a neuron can be excited by the chemical synapse or the memristive synapse for generating chaotic firing patterns. Oscillation of the circuit composed of neuron and functional synapse is analyzed, suggesting that there exists a relation between the local activity and the edge of chaos via Hopf bifurcation. A modular circuit is designed to construct large-scale neural network. These results in this paper provide new evidences for application of memristive components and guide us to know the biophysical function of chemical synapse from physical viewpoint, in which the chemical synapse could be a kind of memristive synapse because of the same biophysical function.

     

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.

     

Anticipating spike synchronization in nonidentical chaotic neurons

Anticipating synchronization is investigated in nonidentical chaotic systems unidirectionally coupled in a master-slave configuration without a time-delay feedback. We show that if the parameters of chaotic master and slave systems are mismatched in such a way that the mean frequency of a free slave system is greater than the mean frequency of a master system, then the phase synchronization regime can be achieved with the advanced phase of the slave system. In chaotic neural systems, this leads to the anticipating spike synchronization: unidirectionally coupled neurons synchronize in such a way that the slave neuron anticipates the chaotic spikes of the master neuron. We demonstrate our findings with coupled Rössler systems as well as with two different models of coupled neurons, namely, the Hindmarsh–Rose neurons and the adaptive exponential integrate-and-fire neurons.     

Complete dynamical analysis of a neuron model

In-depth understanding of the generic mechanisms of transitions between distinct patterns of the activity in realistic models of individual neurons presents a fundamental challenge for the theory of applied dynamical systems. The knowledge about likely mechanisms would give valuable insights and predictions for determining basic principles of the functioning of neurons both isolated and networked. We demonstrate a computational suite of the developed tools based on the qualitative theory of differential equations that is specifically tailored for slow–fast neuron models. The toolkit includes the parameter continuation technique for localizing slow-motion manifolds in a model without need of dissection, the averaging technique for localizing periodic orbits and determining their stability and bifurcations, as well as a reduction apparatus for deriving a family of Poincaré return mappings for a voltage interval. Such return mappings allow for detailed examinations of not only stable fixed points but also unstable limit solutions of the system, including periodic, homoclinic and heteroclinic orbits. Using interval mappings we can compute various quantitative characteristics such as topological entropy and kneading invariants for examinations of global bifurcations in the neuron model.     

Dynamic analysis and cryptographic application of a 5D hyperbolic memristor-coupled neuron

In this paper, the dynamic analysis and cryptographic applications of hyperbolic memristor-coupled neurons are reported. A memristor model is proposed, and its locally active property is verified by DC V-I diagram. A 5D hyperbolic memristor-coupled neuron is constructed. The boundedness and Hamiltonian energy of this 5D hyperbolic memristor-coupled neuron are analyzed. The nonlinear behavior of the 5D hyperbolic memristor-coupled neuron such as coexistence bifurcation mode and coexistence attractor is revealed by the bifurcation diagrams and phase diagrams. Furthermore, state switching without parameters is also explored. In order to enhance the security of image transmission, a full-process DNA encryption algorithm based on the proposed 5D hyperbolic memristor-coupled neuron combining with DNA sequence is presented. The histogram and correlation analysis of the encrypted image show that the image encryption algorithm has strong anti-attack ability.

     

Simulating electric activities of neurons by using PSPICE

Electric activities in the Morris–Lecar neuron and Josephson junction coupled resonator are investigated in a numerical way, and electric circuits are also designed by using the Personal Simulation Program with Integrated Circuit Emphasis (PSPICE). Within the improved Morris–Lecar circuit, a new integrator for the ion channel of potassium is designed, and the transition of electric activities, quiescent state to spiking to bursting to quiescent state could be observed. In the circuit of the Josephson-junction coupled resonator, an equivalent circuit is designed to reproduce several types of electric activity. The detailed parameter regions are detected to generate spiking and bursting states in the electric circuits for neurons, and these results are consistent with the numerical results. Bifurcation diagrams for interspike interval (ISI) vs. the forcing current are calculated to detect the excitability of the neuron model.     

Synchrony and lag synchrony on a neuron model coupling with time delay

A neuron model of the Morris and Lecar form is investigated, which is composed of two individuals and is considered to be functioned by the gap junction coupling. When the level of the reversal potential in the calcium ion channel is small, neurons adjust their activities to the common asymptotic states. However, if we increase the level of the reversal voltage in the calcium ion channel, the exact synchrony firing of neurons is produced. Patterns of synchrony activity and the stability are observed to vary with the choice of time delay, which also enhances the multi-variety of the spike bursting firing rhythm. The lag synchrony of time trajectories of the voltage is illustrated near the boundary of the synchrony regime.     

认知神经科学中蕴藏的力学思想与应用

该文系统总结了作者团队在脑科学领域内提出的神经能量理论与方法,以及力学与神经能量理论之间的内在联系.着重介绍了如何运用分析动力学的思想构建一个与H-H模型等效的W-Z神经元模型.并以此为基础,在神经科学领域内提出了以神经能量为核心的大尺度神经科学模型和大脑全局神经编码的理论框架.在包括视知觉等多个感知觉神经系统的信息处理、大脑的智力探索以及预测神经元新的工作机制、解释神经科学难以解释的实验现象等方面,证实了这个新颖的神经元模型所展现出来的独特功能与优势.由于可塑性是认知神经科学与智能行为的核心,通过蛋白质分子机器的经典力学分析,进一步阐明了神经元的可塑性和神经发育不仅仅只是生物化学反应过程,力学的作用与贡献也是不可或缺的重要因素.表明了力学科学在神经科学、生命科学中的研究思想及其内在逻辑的深远影响.这些研究对于今后推动实验神经科学与理论神经科学的融合,摒弃神经科学领域中还原论与整体论研究方法中的不足,并将它们各自的优点进行有效地整合,促进力学科学的理论与方法的渗透是极其重要的.      

Experimental realizations of the HR neuron model with programmable hardware and synchronization applications

This study presents experimental realizations of the HR neuron model with programmable hardware and synchronization applications. The HR neuron model exhibiting burst, spike, and chaotic dynamics has been implemented with both FPAA (Field Programmable Analog Array) and FPGA (Field Programmable Gate Array) devices. These devices provide flexible design possibilities such as reducing the complexity of design, real-time modification, software control and adjustment within the system. And it is also examined experimentally that how the synchronization of two HR neurons are able to achieve by using these hardware. The experimental results obtained from FPAA and FPGA based realizations agree with the numerical simulations very well.     

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.      

Synchronization behavior of coupled neuron circuits composed of memristors

The fluctuation of intracellular and extracellular ion concentration induces the variation of membrane potential, and also complex distribution of electromagnetic field is generated. Furthermore, the membrane potential can be modulated by time-varying electromagnetic field. Therefore, magnetic flux is proposed to model the effect of electromagnetic induction in case of complex electrical activities of cell, and memristor is used to connect the coupling between membrane potential and magnetic flux. Based on the improved neuron model with electromagnetic induction being considered, the bidirectional coupling-induced synchronization behaviors between two coupled neurons are investigated on Spice tool and also printed circuit board. It is found that electromagnetic induction is helpful for discharge of neurons under positive feedback coupling, while electromagnetic induction is necessary to enhance synchronization behaviors of coupled neurons under negative feedback coupling. The frequency analysis on isolate neuron confirms that the frequency spectrum is enlarged under electromagnetic induction, and self-induction effect is detected. These experimental results can be helpful for further dynamical analysis on synchronization of neuronal network subjected to electromagnetic radiation.     

The race to the nociceptor: mechanical versus temperature effects in thermal pain of dental neurons

The sensing of hot and cold stimuli by dental neurons differs in several fundamental ways. These sensations have been characterized quantitatively through the measured time course of neural discharge signals that result from hot or cold stimuli applied to the teeth of animal models. Although various hypotheses have been proposed to explain the underlying mechanism, the ability to test competing hypotheses against experimental recorded data using biophysical models has been hindered by limitations in our understanding of the specific ion channels involved in nociception of dental neurons. Here we apply recent advances in established biophysical models to test the competing hypotheses. We show that a sharp shooting pain sensa-tion experienced shortly following cold stimulation cannot be attributed to the activation of thermosensitive ion channels, thereby falsifying the so-called neuronal hypothesis,which states that rapidly transduced sensations of coldness are related to thermosensitive ion channels. Our results support a central role of mechanosensitive ion channels and the associated hydrodynamic hypothesis. In addition to the hydrodynamic hypothesis, we also demonstrate that the long time delay of dental neuron responses after hot stimulation could be attributed to the neuronal hypothesis—that a relatively long time is required for the temperature around nociceptors to reach some threshold. The results are useful as a model of how multiphysical phenomena can be combined to provide mechanistic insight into different mechanisms underlying pain sensations.     

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities： experiments and analysis

Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one- or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities （stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.）. Thirdly, different types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.