一个小波函数指数参数变化的分岔现象

研究一个高斯小波函数产生的混沌分岔现象.随着小波函数中指数参数的增加，它的分岔图出现了倍周期分岔，然后出现混沌，经过一段混沌区域后又出现2的幂周期.在整个过程中，正分岔与逆分岔完整地结合在一起.改变小波函数的系数出现一些明显的奇数周期，如3周期、5周期等.绘制Lyapunov指数曲线及映射折射过程，对混沌现象进行研究.将小波函数展开成近似的多项式函数，对近似多项式函数的分岔图进行了分析. 关键词： 混沌 分岔 小波函数     

演示离散混沌系统分岔图的实验方法

将模拟器件和数字器件相结合,以一维Logistic映象和二维 Henon映象为例,介绍了在电路上实现离散系统分岔图的方法,实验结果与数值计算的结果非常一致.     

logistic模型的倍周期分岔控制

研究了logistic模型的倍周期分岔的控制问题，设计了各种线性控制器，得到了系统在控制前和控制后的分岔图，改变了动力系统的分岔特性.根据实际的应用目的可以设计不同的控制器，使倍周期分岔延迟或提前出现，甚至消失.适当选择控制器增益可以使分岔控制的效果更好. 关键词： logistic模型 倍周期分岔 分岔控制 控制器     

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh–Rose neuron model

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh-Rose （HR） neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two- dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the determin- istic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in dif- ferent two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.     

Time series-based bifurcation diagram reconstruction

We consider the problem of reconstructing bifurcation diagrams (BDs) of maps using time series. This study goes along the same line of ideas presented by Tokunaga et al. [Physica D 79 (1994) 348] and Tokuda et al. [Physica D 95 (1996) 380]. The aim is to reconstruct the BD of a dynamical system without the knowledge of its functional form and its dependence on the parameters. Instead, time series at different parameter values, assumed to be available, are used. A three-layer fully-connected neural network is employed in the approximation of the map. The task of the network is to learn the dynamics of the system as function of the parameters from the available time series. We determine a class of maps for which one can always find a linear subspace in the weight space of the network where the network’s bifurcation structure is qualitatively the same as the bifurcation structure of the map. We discuss a scheme in locating this subspace using the time series. We further discuss how to recognize time series generated by this class of maps. Finally, we propose an algorithm in reconstructing the BDs of this class of maps using predictor functions obtained by neural network. This algorithm is flexible so that other classes of predictors, apart from neural networks, can be used in the reconstruction.     

Characteristics of critical amplitude of a sinusoidal stimulus in a model neuron

The characteristics of the critical amplitude of a sinusoidal stimulus in a model neuron, Morris－Lecar model, are investigated numerically. It is important in the study of stochastic resonance to determine whether a periodic stimulus is subthreshold or not. The critical amplitude as a function of the stimulus frequency is not a constant, but a curve, which is the boundary between subthreshold and suprathreshold stimulation. It has been considered that this curve is U-shaped in the previous investigations, and this has been accepted as a universal phenomenon. Nevertheless, we think that it is only true for a type of neuron: namely, resonators. Actually, there exists another type of neuron, integrators, which can undergo a saddle-node on invariant circle bifurcation from the rest state to the firing state. For the latter we find that the critical amplitude increases monotonically as the frequency of sinusoidal stimulus is increased. This is shown by way of the Morris－Lecar model. As a consequence, the critical amplitude curve is studied further, and the dynamical mechanisms underlying the change in critical amplitude curve are uncovered. The results of this paper can provide a reference to choose the subthreshold periodic stimulus.     

Dynamics of a neuron model in different two-dimensional parameter-spaces

We report some two-dimensional parameter-space diagrams numerically obtained for the multi-parameter Hindmarsh-Rose neuron model. Several different parameter planes are considered, and we show that regardless of the combination of parameters, a typical scenario is preserved: for all choice of two parameters, the parameter-space presents a comb-shaped chaotic region immersed in a large periodic region. We also show that exist regions close these chaotic region, separated by the comb teeth, organized themselves in period-adding bifurcation cascades.     

时滞惯性神经网络的稳定性和分岔控制

针对一类二阶时滞惯性神经网络模型,提出一种基于时滞反馈的分岔控制方法.利用时滞微分方程动力学理论,给出反馈控制系统的稳定性以及发生Hopf分岔的判别条件.数值仿真显示所设计的控制器不仅能有效延迟网络分岔的发生,还能扩大稳定域并改善网络的收敛速度.     

Hopf bifurcation analysis of Chen circuit with direct time delay feedback

Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, Hopf bifurcation in the circuit is analysed using the Hopf bifurcation theory and the central manifold theorem in this paper. Bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodical orbit (oscillation) in Chen circuit with direct time delay feedback. Bifurcation boundaries are derived using the Hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit.     

Stability and Neimark-Sacker bifurcation analysis of a food-limited population model with a time delay

In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.     

Phase diagram of speed gradient model with an on-ramp

In this paper, phase transitions are investigated in speed gradient model with an on-ramp. Phase diagrams of traffic flow composed of manually driven vehicles and adaptive cruise control (ACC) vehicles are studied, respectively. The traffic flow composed of ACC vehicles is modeled by enhancing propagation speed of small disturbance. The phase diagram of traffic flow composed of manually driven vehicles is similar to that in previous works, in which such states as pinned localized cluster (PLC), moving localized cluster (MLC), triggered stop-and-go traffic (TSG), oscillatory congested traffic (OCT), and homogeneous congested traffic (HCT) are reproduced. In the phase diagram of traffic flow composed of ACC vehicles, traffic stability is enhanced and such states as PLC, MLC, and TSG disappear. Furthermore, some interesting phenomena, such as stationary OCT upstream of on-ramp and appearance of second OCT in HCT, are identified.     

镶嵌正方晶格上Gauss模型的相图

利用等效变换和自旋重标相结合的方法, 研究了镶嵌正方晶格上的Gauss模型. 研究 发现, 该系统可以变换为正方晶格上具有最近邻和次近邻相互作用的Gauss系统, 由此严格求得了镶嵌正方晶格上Gauss模型的临界温度, 得到了该系统的精确相图.     

Experimental bifurcation diagram of a solid state laser with optical injection

A method is presented for the automatic construction of an experimental bifurcation diagram of an optically injected solid state laser. From measured time series of laser output intensity, different identifiers of aspects of the dynamics are derived. Combinations of these identifiers are then used to characterize different possible bifurcations. The resulting experimental bifurcation diagram in the plane of injection strength versus detuning includes saddle-node, Hopf, period-doubling and torus bifurcations. It is shown to agree well with a theoretical bifurcation analysis of a corresponding rate equation model.     

具有自适应反馈突触的神经元模型中的混沌:电路设计

近期文献中报道了在具有自适应反馈突触的神经元模型中,随着参数的变化,存在从两个共存吸引子到一个相连吸引子再到两个共存吸引子的混沌转化现象.本文对此模型进行了电路设计,同时对具有非单调激活函数功能的电路设计进行了细致的研究,并利用Electronic Workbench (EWB)软件对所设计的电路进行了仿真实验,研究了电路中的混沌现象,验证了所设计电路的动力学行为与通过数值模拟结果十分相似. 关键词： 自适应反馈突触 神经元模型 混沌 电路设计     

分数阶FitzHugh-Nagumo模型神经元的动力学特性及其同步

通过对分数阶FitzHugh-Nagumo模型神经元的研究,当外加电流强度作为分岔参数时,发现这种模型神经元从静息态到周期放电态所经历的Hopf分岔点不同于相应的整数阶模型神经元的分岔点;而且分数阶FitzHugh-Nagumo模型神经元呈现周期放电的外加电流强度的范围比相应的整数阶模型神经元的范围小,然而放电频率却比相应的整数阶模型神经元的放电频率高.同时还揭示在周期放电的情况下分数阶FitzHugh-Nagumo模型神经元之间的同步速率比相应的整数阶模型神经元之间的同步速率快.在数值模拟分数阶微分方程 关键词： 分数阶 Hopf分岔 FitzHugh-Nagumo模型 同步     

一维扩展离子Hubbard模型的相图研究

应用密度矩阵重整化群方法, 研究了存在交错离子势Δ时一维半满扩展Hubbard模型的相图. 通过计算关联函数、结构因子、位置算符等方法, 描绘了从Mott绝缘体-键有序绝缘体-Band 绝缘体的特性并给出了精确的相边界. 研究发现: 中间的键有序绝缘体相在相图中占据了很小的一部分区域, 当存在离子势Δ的情况下, 这个区域将会有所增大; 而当相互作用足够强时, 这个中间相消失. 给出了离子Hubbard模型(最近邻电子-电子相互作用V=0)的相图.     

Stability and Neimark-Sacker bifurcation analysis of food-limited population model with time delay

In this paper, a kind of discrete delay food-limited model obtained by Euler method is investigated, where the discrete delay τ is regarded as a parameter. By analyzing the associated characteristic equation, the linear stability of this model is studied. It is shown that Neimark-Sacker bifurcation occurs when τ crosses some critical values. The explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form. Finally, numerical simulations are performed to verify the analytical results.     

Control of firing activities in thermosensitive neuron by activating excitatory autapse

Temperature has distinct influence on the activation of ion channels and the excitability of neurons, and careful change in temperature can induce possible mode transition in the neural activities. The formation and development of autapse connection to neuron can enhance its self-adaption to external stimulus, and thus the firing patterns in neuron can be controlled effectively. The autapse is activated to drive a thermosensitive neuron, which is developed from the FitzHugh–Nagumo neural circuit by incorporating a thermistor, and the dynamics in the neural activities is explored to find mode dependence on the temperature and autaptic current. It is found that the firing modes can be controlled by temperature, and the neuron is wakened from resting state to periodic oscillation with the increase of temperature. Furthermore, the intensity and the intrinsic time delay in the autapse are respectively adjusted to control the neural activities, and it is confirmed that appropriate setting for autaptic current can balance and enhance the temperature effect on the neural activities.     

最小神经元模型放电起始动态控制与分析

本文采用最小神经元模型,从生理学角度设计wash-out滤波器,实现了不同放电起始动态机理之间的转换,并证明wash-out滤波器控制通过影响阈下电流的竞争结果改变了神经元的放电起始动态机理. 关键词： 放电起始动态机理 阈下电流竞争 最小神经元模型 wash-out滤波器     

An implementation of cellular automaton model for single-line train working diagram

According to the railway transportation system's characteristics, a new cellular automaton model for the single-line railway system is presented in this paper. Based on this model, several simulations were done to imitate the train operation under three working diagrams. From a different angle the results show how the organization of train operation impacts on the railway carrying capacity. By using the non-parallel train working diagram the influence of fast-train on slow-train is found to be the strongest. Many slow-trains have to wait in-between neighbouring stations to let the fast-train(s) pass through first. So the slow-train will advance like a wave propagating from the departure station to the arrival station. This also resembles the situation of a highway jammed traffic flow. Furthermore, the nonuniformity of travel times between the sections also greatly limits the railway carrying capacity. After converting the nonuniform sections into the sections with uniform travel times while the total travel time is kept unchanged, all three carrying capacities are improved greatly as shown by simulation. It also shows that the cellular automaton model is an effective and feasible way to investigate the railway transportation system.