Noise-Induced Transition in a Voltage-Controlled Oscillator Neuron Model

In the presence of Gaussian white noise, we study the properties of voltage-controlled oscillator neuron model and discuss the effects of the additive and multiplicative noise. It is found that the additive noise can accelerate and counterwork the firing of neuron, which depends on the value of central frequency of neuron itself, while multiplicative noise can induce the continuous change or mutation of membrane potential.     

Noise-Induced Phase Transition in Traffic Flow

One of the dynamic phases of the traffic flow is the traffic jam. It appears in traffic flow when the vehicledensity is larger than the critical value. In this paper, a new method is presented to investigate the traffic jam when thevehicle density is smaller than the critical value. In our method, we introduce noise into the traffic system after sufficienttransient time. Under the effect of noise, the traffic jam appears, and the phase transition from tree to synchronized flowoccurs in traffic flow. Our method is tested for the deterministic NaSch traffic model. The simulation results demonstratethat there exist a broad range of lower densities at which the noise effect leading to traffic jam can be observed.     

Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

In this paper,by the help of evolutionary algorithm and using Hindmarsh–Rose(HR)neuron model,we investigate the efect of topology structures on synchronization transition between diferent states in coupled neuron cells system.First,we build diferent coupling structure with N cells,and found the efect of synchronized transition contact not only closely with the topology of the system,but also with whether there exist the ring structures in the system.In particular,both the size and the number of rings have greater efects on such transition behavior.Secondly,we introduce synchronization error to qualitative analyze the efect of the topology structure.Furthermore,by fitting the simulation results,we find that with the increment of the neurons number,there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems.Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system.Biological system may gradually acquire such efcient topology structures through the long-term evolution,thus the systems’information process may be optimized by this scheme.     

Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

In this paper, by the help of evolutionary algorithm and using Hindmarsh-Rose (HR) neuron model, we investigate the effect of topology structures on synchronization transition between different states in coupled neuron cells system. First, we build different coupling structure with N cells, and found the effect of synchronized transition contact not only closely with the topology of the system, but also with whether there exist the ring structures in the system. In particular, both the size and the number of rings have greater effects on such transition behavior. Secondly, we introduce synchronization error to qualitative analyze the effect of the topology structure. Furthermore, by fitting the simulation results, we find that with the increment of the neurons number, there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems. Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system. Biological system may gradually acquire such efficient topology structures through the long-term evolution, thus the systems' information process may be optimized by this scheme.     

Hindmarsh-Rose神经元的随机自共振和噪声影响下的同步

研究了噪声对Hindmarsh-Rose(HR)神经元随机自共振和同步的影响。将高斯白噪声加入HR神经元模型的膜电位上，把外界直流电作为分岔参数，分别考虑参数处于Hopf分岔前、Hopf分岔附近和Hopf分岔后时，噪声影响下的随机自共振现象。两个未经耦合的全同HR神经元，如果接受相同的噪声激励，只要噪声强度高于某临界值，就能达到完全同步。进一步，噪声能够增强弱耦合神经元的完全同步。数值结果表明簇放电的神经元比峰放电的神经元更容易被噪声诱导而达到完全同步，耦合也增强了神经元对噪声激励的灵敏度。     

Coherence resonance and synchronization of Hindmarsh-Rose neurons with noise

Noise effects on coherence resonance and synchronization of Hindmarsh-Rose (HR) neuron model are studied. The coherence resonance of a single HR neuron with Gaussian white noise added to the membrane potential is investigated in situations before, near and after the Hopf bifurcation, separately, with the external direct current as a bifurcation parameter. It is shown that even though there is no coupling between neurons, uncoupled identical HR neurons driven by a common noise can achieve complete synchronization when the noise intensity is higher than a critical value. Furthermore, noise also enhances complete synchronization of weakly coupled neurons. It is concluded that synchronization in bursting neurons is easier to be induced than in spiking ones, and coupling enhances the sensitivity of synchronization of neurons to noise stimulus.     

First-Order-Like Transition in Inhomogeneously Broadened Two-Mode Ring Laser Gain-Noise Model

An inhomogeneously broadened two-mode ring laser gain-noise model taking account of both full saturation effects and multiplicative noise induced by gain fluctuations is investigated. By using a corresponding Fokker-Planck equation and perturbation theory proposed by Graham et al. the joint stationary distribution for light intensities is obtained. It is found that a first-order-like transition occurs when laser is operated off resonance.     

基于Duffing振子的变尺度微弱特征信号检测方法研究

研究了Holmes型Duffing方程的混沌特性用于信号检测的方法,针对该方法只适用检测特定频率成分信号、方程参数选择不便以及噪声影响检测结果等情况,提出基于Duffing振子的变尺度微弱特征信号检测方法. 数值分析表明,该方法可以仅用一组确定的参数条件,检测任意频率、任意相位的特征信号.     

Dynamical Phase Transition in a Neural Network Model with Noise: An Exact Solution

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same value. It is shown that, under very general conditions, there exists a critical value _c of the noise, below which the network remains organized and above which it behaves randomly. The existence and nature of the phase transition are computed analytically, showing that the critical exponent is 1/2. The dependence of _c on the parameters of the network is obtained. These results are then compared with two numerical realizations of the network.     

类锂离子(Z=11～20)1s22s-1s24p的跃迁能和振子强度

利用全实加关联方法计算了类锂离子(Z=11～20)激发态1s^24p的能量及精细结构,同时计算了1s^22s-1s^24p的跃迁能和振子强度．非相对论能量用Rayleigh-Ritz变分法确定;相对论和质量极化效应修正用微扰论计算;量子电动力学修正用有效核电荷方法计算．在能级精细结构的计算中不仅考虑了自旋-轨道相互作用还计及自旋-其他轨道相互作用．将得到的计算结果和已有实验数据及物理规律进行了比较．     

Optimal Force Mismatch for Fluctuation-Activated Transition in a System of Two Coupled Bistable Oscillators

We study the fluctuation-activated transition process in a system of two coupled forced bistable oscillators with a mismatch σ in the force constants. As the coupling strength μ is increased, the transition pathway undergoes four stages changes from a two-step process with two candidate pathways to a mixture of a two-step pathway and a one-step pathway to a one-step process with also two candidate pathways and then to a one-step process with a single pathway.Interestingly, we find that the total transition rate depends nonmonotonically on σ in the weak coupling: a maximal rate appears in an intermediate magnitude of σ. Moreover, the rate also exhibits an unexpected maximum as a function ofμ. The results are in an excellent agreement with our numerical simulations by forward flux sampling.     

白交叉关联色噪声驱动的线性振子的扩散

研究了由白交叉相关的两色噪声所驱动的线性振子的扩散,其中一个噪声受偏置的周期信号所调制.揭示了乘性色噪声的自关联时间τ1和加性色噪声的自关联时间τ2对d-Q,d-D及d-Ω曲线的影响,其中d,Q,D和Ω分别为振子的扩散系数、受信号调制的噪声强度、未受调制的噪声强度和信号的频率.发现d-Q和d-D曲线均存在一个极小值,而d-Ω曲线则在Ω=～Ω处呈现极大值,～Ω为振子频率.推导了使扩散系数d=0的条件.     

Unitary Operator and Density Matrix for a Ring of Coupled Oscillator Model

A unitary operator U which can directly diagonalize the Hamiltonian of a ring of N coupled oscillators is found. With use of the technique of integration within an ordered product of operators we see that U includes a squeezing transformation. For large N it turns out that, except a zero-mode, the ring Hamiltonian has the same spectrum as the one-dimensional monatomic lattice model plus the Born-Von-Karmen boundary condition. The density matrix of this model is calculated by the U transformation, which further leads us to derive the heat capacity of the coupled oscillators in the large N limit.     

DKP Oscillator in a Noncommutative Space

We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter.     

Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic field is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti-Jaynes-Cummings (AJC) or Jaynes-Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic field) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit.     

Colored Noise in First-order-like Phase Transition of a Laser System

The decoupling theory is employed to analyze the multiplicative colored noise in a single mode laser system. Steady state intensity distribution function is derived when colored noise is included in the laser system. The first-order-like phase transition driven by multiplicative colored noise is investigated and compared with the case of multiplicative white noise. It is shown that the noise correlation time can affect the parameter plane of the first-order-like phase transition. The steady state intensity distributions in a laser system is changed greatly with noise correlation time τ.     

DKP Oscillator in a Noncommutative Space

We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein-Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter.     

Bifurcation and Entropy Analysis of a Chaotic Spike Oscillator Circuit Based on the S-Switch

This paper presents a model and experimental study of a chaotic spike oscillator based on a leaky integrate-and-fire (LIF) neuron, which has a switching element with an S-type current-voltage characteristic (S-switch). The oscillator generates spikes of the S-switch in the form of chaotic pulse position modulation driven by the feedback with rate coding instability of LIF neuron. The oscillator model with piecewise function of the S-switch has resistive feedback using a second order filter. The oscillator circuit is built on four operational amplifiers and two field-effect transistors (MOSFETs) that form an S-switch based on a Schmitt trigger, an active RC filter and a matching amplifier. We investigate the bifurcation diagrams of the model and the circuit and calculate the entropy of oscillations. For the analog circuit, the “regular oscillation-chaos” transition is analysed in a series of tests initiated by a step voltage in the matching amplifier. Entropy values are used to estimate the average time for the transition of oscillations to chaos and the degree of signal correlation of the transition mode of different tests. Study results can be applied in various reservoir computing applications, for example, in choosing and configuring the LogNNet network reservoir circuits.     

Transition to complete synchronization via near-synchronization in two coupled chaotic neurons

The synchronization transition in two coupled chaotic Morris-Lecar （ML） neurons with gap junction is studied with the coupling strength increasing. The conditional Lyapunov exponents, along with the synchronization errors are calculated to diagnose synchronization of two coupled chaotic ML neurons. As a result, it is shown that the increase in the coupling strength leads to incoherence, then induces a transition process consisting of three different synchronization states in succession, namely, burst synchronization, near-synchronization and embedded burst synchronization, and achieves complete synchronization of two coupled neurons finally. These sequential transitions to synchronization reveal a new transition route from incoherence to complete synchronization in coupled systems with multi-time scales.     

引入Polyakov环路的手征模型中的涨落与相变

We explore the NJL model with Polyakov loops for a system of three colors and two flavors within the mean-field approximation, where both chiral symmetry and confinement are taken into account. We focus on the phase structure of the model and study the chiral and Polyakov loop susceptibilities.