细胞丛状化分布对二维耦合体系尺度选择效应的影响

采用随机模拟方法对体系的化学朗之万方程进行了数值模拟，考察了二维耦合细胞体系中，细胞的丛状化分布对于因内噪声作用而产生的尺度选择效应所带来的影响.研究发现，当体系处于Hopf分岔点附近时，由于耦合作用使得处于最佳状态的一定数目的细胞呈现丛状化聚集在一起，而这种丛状化分布的“团队精神”可以极大地提高体系的工作效率，表现为体系对外界刺激信号的响应能力(信噪比)达到极大值.同时还观察到，体系对外界刺激最为敏感时对应的最佳细胞丛尺度大小不随耦合强度的改变而变化，而体系输出信号的信噪比，随着耦合强度的增加有增大趋势.这些现象表明，细胞的丛状化分布将极大地增强细胞中钙离子信号对外界刺激的响应效果.生物体系本身可能具有这种特性，并利用它来改善和提高感受外界信息的能力.     

Quenching problem of globally coupled bistable stochastic systems with finite size

The transient process of globally coupled bistable systems from an unstable state to metastable state (i.e, quenching process) is studied analytically for small noise intensity. The influences of noise intensity and system size on the system evolution are investigated. The problem of a large number of coupled Langevin equations is reduced to a simple problem of a one-dimensional ordinary differential equation, subject to a white noise with intensity explicitly given. The analytical results are fully confirmed by direct numerical computations. Received: 3 July 1997 / Revised: 4 December 1997 / Accepted: 15 January 1998     

外力作用下反馈耦合布朗棘轮的定向输运

本文研究了处于外力作用下双阱棘轮势中两个反馈耦合布朗粒子的定向输运性能. 通过对过阻尼朗之万方程的数值求解, 详细讨论了外力、热噪声与势阱的不对称参数等对耦合布朗粒子的平均速度、 有效扩散系数及Pe数的影响. 研究发现, 平均速度随外力呈周期性的变化规律. 同时耦合系统存在最优噪声强度会使定向输运达到最强. 值得指出的是棘轮系统可通过改变双阱势的结构来获得较强的定向流. 关键词： 耦合布朗棘轮 外力 双阱棘轮势 平均速度     

Selective effects of noise by stochastic multi-resonance in coupled cells system

By investigating a stochastic model for intracellular calcium oscillations proposed by Höfer, we have analyzed the transmission behavior of calcium signaling in a one-dimensional two-way coupled hepatocytes system. It is shown that when the first cell is subjected to the external noise, the output signal-to-noise ratio (SNR) in the cell exhibits two maxima as a function of external noise intensity, indicating the occurrence of stochastic bi-resonance (SBR). It is more important that when cells are coupled together, the resonant behavior in the 1st cell propagates along the chain with different features through the coupling effect. The cells whose locations are comparatively close to or far from the 1st cell can show SBR, while the cells located in the middle position can display stochastic multi-resonance (SMR). Furthermore, the number of cells that can show SMR increases with coupling strength enhancing. These results indicate that the cells system may make an effective choice in response to external signaling induced by noise, through the mechanism of SMR by adjusting coupling strength.     

非对称双稳耦合网络系统的尺度随机共振研究

研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象. 关键词： 尺度随机共振 非对称双稳耦合网络系统 余弦信号 矩形信号     

生物构型对耦合Hindmarsh-Rose神经元系统响应能力的影响

利用Hindmarsh-Rose神经元模型研究了真实的生物细胞连接构型对耦合神经元系统响应能力的影响. 外界刺激信号通过细胞耦合从受刺激的神经元传递到其他神经元,合适的生物构型可以提高系统对刺激信号的响应能力和敏感度;同时,生物构型还会影响神经元系统的同步能力以及选择效应. 模拟的结果可以帮助我们理解面对不同外界刺激,生物体会协调自身结构,选择最佳的构型予以响应.     

Dynamical response of a neuron–astrocyte coupling system under electromagnetic induction and external stimulation

Previous studies have observed that electromagnetic induction can seriously affect the electrophysiological activity of the nervous system. Considering the role of astrocytes in regulating neural firing, we studied a simple neuron–astrocyte coupled system under electromagnetic induction in response to different types of external stimulation. Both the duration and intensity of the external stimulus can induce different modes of electrical activity in this system, and thus the neuronal firing patterns can be subtly controlled. When the external stimulation ceases, the neuron will continue to fire for a long time and then reset to its resting state. In this study, "delay" is defined as the delayed time from the firing state to the resting state, and it is highly sensitive to changes in the duration or intensity of the external stimulus. Meanwhile, the self-similarity embodied in the aforementioned sensitivity can be quantified by fractal dimension. Moreover, a hysteresis loop of calcium activity in the astrocyte is observed in the specific interval of the external stimulus when the stimulus duration is extended to infinity, since astrocytic calcium or neuron electrical activity in the resting state or during periodic oscillation depends on the initial state. Finally, the regulating effect of electromagnetic induction in this system is considered. It is clarified that the occurrence of "delay" depends purely on the existence of electromagnetic induction. This model can reveal the dynamic characteristics of the neuron–astrocyte coupling system with magnetic induction under external stimulation. These results can provide some insights into the effects of electromagnetic induction and stimulation on neuronal activity.     

The dynamics of coupled nonlinear model Boltzmann equations

A multispecies gas described by coupled nonlinear Boltzmann equations is studied as a dynamical system. Properties are determined of theN coupled nonlinear ODEs for the number densities obtained from the Boltzmann equations for the spatially uniform system ofN species undergoing binary scattering, removal, and regeneration in the presence of an external force field and a reservoir of background gas. The physically realizable setQ, the nonnegative cone in theN-dimensional phase space of species number densities, is established as invariant under the flow. The fixed-point equations for the ODEs are shown to be equivalent to 2 ^N linear systems, and conditions for the stability and instability of the fixed points are then established. Stable fixed points are demonstrated to exist inQ by showing that they enter via a sequence of transcritical bifurcations as physical parameters are varied. For the two-species case the typical global structure of the solutions is established. Various particular cases are described including one which possesses an infinite family of periodic solutions and one that depends delicately upon initial conditions due to a separatrix that separatesQ into two invariant sets.     

系统规模对群体行为的效果

影响细胞群体行为的因素是多种多样的, 除了以前研究的细胞通讯方式和环境因素外, 还与现有文献没有或很少研究的细胞数目(即系统规模)有关. 本文研究了系统规模对一类合成多细胞通讯系统的聚类行为的影响. 在该系统中, 单个系统是由压制振动子和基于延迟的松弛振子整合而成的振子, 而振子之间通过群体感应机制相互耦合. 通过分岔分析和数值模拟发现: 细胞数目的增加不仅可以改变平衡态聚类稳定性区间的大小并诱导新的聚类行为, 而且有利于扩大平衡态聚类的吸引域, 表明细胞分化可能与系统规模有密切关系; 细胞数目的增加还可以极大地丰富平衡态聚类和振动聚类的表现形式和共存方式, 为生物体对环境的适应性提供了良好的基础. 我们的结果不仅扩充了耦合系统的动力学行为, 也为理解多细胞现象奠定了基础. 关键词： 系统规模 群体感应 群体行为 耦合振子     

Time-dependent molecular fields created by the interaction of an external electro-magnetic field with a molecular system: the derivation of the wave equations

This article continues a previous study (Int. J. Quantum Chem. 114, 1645 (2014)) in which is presented a theory that discusses the possibility to induce a novel field – to be called molecular field – via the interaction of an external electro-magnetic (EM) field and a molecular system. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from three time-space curl equations and one time-space divergence equation to a set of decoupled wave equations usually encountered for fields. In the present study, wave equations are derived for an external field having two features: (1) the field intensity is relatively high enough; (2) the duration of the interaction is short enough.

For this situation, the study reveals that the just mentioned interaction creates two fields that coexist within a molecule: one is just a scalar EM field essentially identical to the external EM field and the other, a vectorial field, produced by the non-adiabatic coupling terms. In addition, we mention that the wave velocities related to these two fields are identical to the wave velocity, c, of the external EM field.     

In- and Anti-transition of Firing Patterns Induced by Random Long-range Connections in Coupled Hindmarsh-Rose Neurons System

研究了在外界刺激电流的作用下,随机的长程关联对耦合的Hindmarsh-Rose神经元放电模式转变的影响．结果表明,当耦合强度较弱时,在神经元网络中加入一定数量的随机的长程关联,神经元的放电模式会从较少的周期态转变到较多的周期态;当耦合强度较强时,在神经元网络中加入一定数量的随机长程关联,神经元的放电模式会产生相反的转变,即从较多的周期态转变到较少的周期态．同时还简单讨论了神经系统的尺度大小和神经元之间的耦合强度,以及不同外界刺激条件下放电模式的强度与临界特性之间的关系．     

Chaotic transition of random dynamical systems and chaos synchronization by common noises

We studied the mechanism behind the connection between the transition to chaos of random dynamical systems and the synchronization of chaotic maps driven by external common noises. Near the chaotic transition, the spatial size of random dynamical systems shows an extreme intermittent behavior. By calculating the scaling exponents, we have found that the origin of this intermittent behavior is on-off intermittency. This led us to conclude that chaotic transitions through on-off intermittency can be regarded as a route for random dynamical systems. To clarify this argument, a two-dimensional random dynamical system and two coupled logistic maps driven by external common noises were analyzed.     

Frequency sensitivity of sub-excitable systems coupled with different topology

We have investigated numerically the behaviours of identical FitzHugh－Nagumo systems, which are coupled into topologies of regular one-dimensional lattice, small-world network and scale-free network, and driven by white noise and an external signal. We found that when a number of uniform systems are coupled into a network, the system's signal-to-noise ratio remains at a high level in a wider frequency range than in the case of a single oscillator. Different architectures manifest different impact, with the scale-free network being the most remarkable. Results presented here suggest a possible approach to improve the sensitivity of a system to external signals and are helpful for designing communication equipments.     

The effect of the size of particles on optical and electrooptical properties of colloids

We have considered optical and electrooptical properties of disperse systems that contain particles with different optical characteristics, sizes, and shapes. Our investigations of the refractive index of a series of disperse systems have shown that, if the particle size does not exceed a few tens of nanometers, the refractive index does not depend on the particle concentration and is equal to the refractive index of a molecular medium that surrounds particles. We have shown that, in an external electric field, systems with these particles almost do not possess birefringence but possess dichroism. Our investigations of systems with a low concentration of particles allowed us to find that the intensity of light transmitted through a Kerr cell that is filled with colloidal particles with a size comparable with the wavelength and that is placed between crossed polarizers varies proportionally to the squared dichroism induced in the colloid by the external field. Linearly polarized light transmitted through this cell in the electric field remains to be linearly polarized, but its plane of polarization rotates by an angle the tangent of which is proportional to the dichroism of the colloid. We propose a method for determining the contributions from birefringence and dichroism to the observed electrooptical effects.     

Generalized <Emphasis Type="Italic">N</Emphasis>-coupled maps with invariant measure in Bose-Mesner algebra perspective

By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with a given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a relation between the vertexes. Based on the E ₀ transverse projection operator, we addressed synchronization problem of an array of the linearly coupled map lattices of identical discrete time systems. The synchronization rate is determined by the second largest eigenvalue of the transition probability matrix. Algebraic properties of the Bose-Mesner algebra with an associated scheme with definite spectrum has been used in order to study the stability of the coupled map lattice. Associated schemes play a key role and may lead to analytical methods in studying the stability of the dynamical systems. The relation between the coupling parameters and the chaotic region is presented. It is shown that the feasible region is analytically determined by the number of couplings (i.e. by increasing the number of coupled maps, the feasible region is restricted). It is very easy to apply our criteria to the system being studied and they encompass a wide range of coupling schemes including most of the popularly used ones in the literature.      

分数阶对数耦合系统在非周期外力作用下的定向输运现象

本文讨论了分数阶对数耦合系统在非周期外力作用情况下, 耦合粒子链的定向输运现象. 由于粒子在黏性介质中的运动具有“记忆性”, 所以本文通过将系统建模为分数阶对数耦合模型来研究各个系统参数对粒子链运动状态的影响. 数值仿真表明: 1)对于此类系统, 只有在存在外力作用的情况下粒子链才能够产生定向输运现象, 并且粒子链平均流速随着外力的增大而增大. 2)对于分数阶阶数较小的系统, 阻尼记忆性对粒子链的运动状态有显著的影响, 具体表现为: 粒子链的平均流速存在上界(这个上界非常小), 无论外力、耦合力以及噪声强度如何变化, 粒子链的平均流速都不会超过这个上界. 当系统的阻尼力很大且外力为零时, 粒子链不会产生定向输运现象. 3) 当系统的阶数与外力较大时, 虽然粒子链能够产生定向流, 但是此时系统对耦合力与噪声具有免疫性. 4) 耦合力与噪声强度对粒子链运动的影响只在外力较小的情况下有所表现. 在这种情况下, 当系统阶数充分大时, 粒子链的平均流速随着耦合力与噪声强度的变化而变化, 并且伴随着定向流的产生.     

The effective gauge field action of a system of non-relativistic electrons

We consider a system of free, non-relativistic electrons at zero temperature and positive density, coupled to an arbitrary, external electromagnetic vector potential,A. By integrating out the electron degrees of freedom we obtain the effective action forA. We show that, in the scaling limit, this effective action is quadratic inA and can be viewed as an integral over the Fermi sphere of effective actions of (1+1)-dimensional, chiral schwinger models. We use this result to elucidate Luther-Haldane bosonization of systems of non-relativistic electrons. We also study systems of weakly coupled interacting electrons for which the BCS channel is turned off. Using the quadratic dependence of the effective action onA, we show that, in the scaling limit, the RPA yields the dominant contribution.     

Modelling collective opinion formation by means of active Brownian particles

The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, the opinion change of the individuals is given by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit holding for fast communication we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) changes the ratio between minority and majority, until above a critical external support the supported subpopulation exists always as a majority. Spatial effects lead to two critical “social” temperatures, between which the community exists in a metastable state, thus fluctuations below a certain critical wave number may result in a spatial opinion separation. The range of metastability is particularly determined by a parameter characterizing the individual response to the communication field. In our discussion, we draw analogies to phase transitions in physical systems. Received 26 November 1999     

A fusion algorithm for infrared and visible images based on RDU-PCNN and ICA-bases in NSST domain

The aim of infrared and visible image fusion is to enhance the feature in infrared image and preserve abundant detail information in visible image. Based on the fact that the human sense system accepts external stimulation only when the stimulus intensity is greater than a certain value and the reaction of neuronal cells have obvious regional characters, an image fusion algorithm based on region dual-channel unit-linking pulse coupled neural networks (RDU-PCNN) and independent component analysis (ICA) bases in non-subsampled shearlet transform (NSST) domain for infrared and visible images is proposed. RDU-PCNN we constructed has obvious regional characters and much lower computational costs. We trained ICA-bases using a number of images that the content and statistical properties are similar with the fusion images but applied it as low-frequency ICA-bases, which can reduce calculation complexity. Experimental results demonstrate that the proposed method can significantly improved the fusion quality and need less computational costs.