State-to-State Transitions in a Hindmarsh-Rose Neuron System

We investigate the dynamical response of the neuron system to a feeble external signal by using the Hindmarsh-Rose model, when the system is tuned below the first bifurcation point, which corresponds to the period-1 bursting state, and an external signal with a fixed period of about 170s is introduced to the system. It is found that to respond to the outside signal, the system changes from the period-1 state to a period-2 one with variation of the signal amplitude, indicating the occurrence of state-to-state transition （SST）. Moreover, when a signal with different fixed periods is introduced, we can also find a similar transition between other states. Furthermore, the effect of the frequency of the signal on the transition is also discussed. These results may imply that SST plays a constructive role in information processing in neuron systems.     

一类可变禁区的不连续系统的加周期分岔

研究了一类可变禁区不连续系统的加周期分岔行为, 发现由可变禁区导致不同类型的加周期分岔. 研究表明, 系统的迭代轨道和禁区的上下两个边界均可发生边界碰撞, 从而产生加周期分岔. 基于边界碰撞分岔理论, 定义基本的迭代单元, 解析推导出了相应的分岔曲线, 在全参数空间中给出了不同加周期所出现的范围. 与数值模拟结果比较, 理论分析结果与数值结果高度一致.     

Co-existence of multiple attractors in the PWM controlled DC drives

DC shunt and series drives are extensively used in the industry. The occurrence of bifurcation and chaos in dc shunt and permanent magnet drives are well known. It is observed that the behavior of the drives not only depends on the value of system parameters but also on the value of initial conditions. Multiple attractors can exist for same parameter value. Different choice of initial conditions gives different periodic behavior of the system. The drive is intended to operate in a parameter range to give period-1 behavior. We report the existence of sub- harmonic oscillations in the period-1 region of the bifurcation diagram along with co-existing attractor with fractal basin boundaries in PWM controlled dc series drives. The series drive is extensively used in electric traction and other applications. The dc drives are run with dc input voltage. This dc voltage may be derived from a dc source or an ac source with a rectifier. The dc series drive shows different bifurcation behavior when different types of input voltage and switching elements are used. The existence of period-1, period-2 and period-4 orbits are observed with different initial conditions in the desired period-1 region of the bifurcation diagram. The dependence of system’s behavior on initial condition may render the system’s behavior unpredictable. These phenomena may have serious implication in performance.     

一类新的混沌神经放电的动力学特征的实验和数学模型研究

神经元电活动理论模型Hindmarsh-Rose(HR)模型提示有位于周期1和周期2放电模式之间的一类特殊的混沌放电,但长期以来对其没有获得足够认识.依据回归映射的确定性结构和非线性预报的短期可预报性,确认了在大鼠的实验性神经起步点的实验中发现的位于周期1和周期2放电模式之间的非周期放电是混沌放电模式,还将该混沌放电模式区分为3个不同表观样式.其中1个表观形式与HR模型的仿真结果相类似,验证了HR模型的理论预期;其余2个样式与仿真结果并不相似.进一步揭示了3个表观样式的动力学特征以及相互之间的区别与联系,并与位于周期2和周期3节律之间、周期3和周期4节律之间的混沌比较了异同,也区别了从周期1到混沌再到周期2放电模式的节律转迁历程与其他的从周期1到周期2节律的分岔过程的不同.研究结果确认了该类特殊混沌节律和相应分岔过程的新特征,丰富了混沌放电节律和节律分岔序列的种类.还对仿真该混沌的多样性和非光滑特性,以及揭示该类混沌的产生途径等进行了讨论. 关键词： 混沌 神经放电模式 分岔 节律     

Oscillations and chaos in CO+O(2) combustion

The gas-phase reaction between carbon monoxide and oxygen (in the presence of small amounts of hydrogen) shows bistability and oscillatory behavior. Typically, the oscillatory ignition has a period-1 relaxation waveform. The limit cycle is born at a saddle-node loop and terminates via a supercritical Hopf bifurcation. For a mean residence time of 8 s there is a period-doubling to a period-2 solution followed by period-halving to quasisinusoidal period-1 oscillations. At longer residence times, more period-doublings forming a full cascade to chaos with subsequent periodic windows are observed. The chaotic attractor has an underlying single-humped next maximum map.     

谷值V~2控制Boost变换器的精确建模与动力学分析

建立了谷值V2控制Boost变换器的离散迭代映射模型,在此基础上得到了输入电压、输出电容及其等效串联电阻(equivalent series resistance,ESR)变化时的分岔图,推导了不动点处的雅可比矩阵,利用特征值和最大Lyapunov指数对系统进行了稳定性分析,并验证了分岔图的正确性.重点研究了输入电压和输出电容及其ESR对谷值V2控制Boost变换器的动力学特性的影响.研究结果表明,输入电压增大时,变换器从周期1态经历1次倍周期分岔和边界碰撞分岔进入混沌状态;输出电容及其ESR具有相同的分岔路由,随着输出电容及其ESR的逐渐减小,变换器具有从周期1态经历周期2态、周期4态、周期8态、逐渐演变到混沌态的动力学行为.最后,用仿真和实验结果验证了本文理论分析的正确性.     

Sensitive signal detection using a feed-forward oscillator network

We present the results of an experimental investigation of a network of nonlinear coupled oscillators which are coupled in feed-forward mode. By exploiting the nonlinear response of each oscillator near its intrinsic Hopf bifurcation point, we have found remarkable amplification of small signals over a narrow bandwidth with a large dynamic range. The effect is exploited to extract a small amplitude periodic signal from an input time series which is dominated by noise. Specifically, we have used this relatively simple experimental system to measure responses with a bandwidth of approximately 1% of the central frequency, amplifications of approximately 60 dB, and a dynamic range of approximately 80 dB and can extract signals from a time series with a signal to noise ratio of approximately -50 dB.     

电压型双频率控制开关变换器的动力学建模与多周期行为分析

在断续导电模式下, 建立了电压型双频率控制开关变换器的动力学模型, 并推导了相应的特征值方程. 根据动力学模型, 采用分岔图研究了电路参数变化时变换器存在的边界碰撞分岔行为和周期2, 周期3,周期4等多周期行为, 结果表明: 变换器经历了周期1态、多周期态、周期1态的分岔路由; 周期态的转变均是由边界碰撞分岔引起的. 根据特征值方程, 采用Lyapunov指数研究了变换器的稳定性, 结果表明: 随着电路参数的变化, Lyapunov指数始终小于零, 变换器一直工作于稳定的周期态, 验证了电压型双频率控制开关变换器的周期3行为并不意味着变换器会必然发生混沌. 通过电路仿真, 分析了负载变化时变换器的时域波形、相轨图和频谱图, 验证了动力学模型的可行性和理论分析的正确性. 实验结果验证了文中的仿真结果. 关键词： 开关变换器 双频率控制 边界碰撞分岔 多周期行为     

Odd periodic window and bifurcations on 2D parameter space of low frequency oscillations

Low frequency current oscillations have been usually investigated under the influence of the external applied voltage, temperature and illumination. A parallel applied magnetic field has been used in the present work in order to obtain odd periodic windows and bifurcations inside them in a two dimension parameter space for a semi-insulating GaAs sample grown by molecular beam epitaxy. Two kinds of parameter spaces have been used in order to stabilize the odd periodic windows and the bifurcations, namely, the external applied voltage versus the parallel magnetic field and the illumination versus the parallel magnetic field. We report on a successful observation of stable cycles of periodicity 3, 4, 5, 6, 7 and 8 inside a period-3 window. An example of bifurcation route is presented following the sequence from chaos to 4, 3, 6, 3, 5, 7, 5, and back to chaos in the parameter space of voltage versus magnetic field. For this bifurcation route we will show which branch of the cycle is bifurcating and which are coalescing with the control parameters.     

Deterministically generated noise amplification in the period-doubling bifurcations of an additive-pulse mode-locked laser

We examine the noise behavior of an additive-pulse mode-locked (APM) laser as it undergoes a period-one/period-two pitchfork bifurcation. We find evidence of noise amplification, “wiggly” bifurcation phenomena, and frequency shifting of the signal within the noise background. The total amount of frequency tuning is about 5.5% of the fundamental frequency.     

Chaos in a chemical system

Chaotic oscillations have been observed experimentally in dual-frequency oscillator OAP - Ce⁺⁴-BrO^? ₃-H₂SO₄ in CSTR. The system shows variation of oscillating potential and frequencies when it moves from low frequency to high frequency region and vice-versa. It was observed that system bifurcate from low frequency to chaotic regime through periode-2 and period-3 on the other hand system bifurcate from chaotic regime to high frequency oscillation through period-2. It was established that the observed oscillations are chaotic in nature on the basis of next amplitude map and bifurcation sequences.     

n-scroll chaotic attractors from a first-order time-delay differential equation

In this paper, a novel first-order delay differential equation capable of generating n-scroll chaotic attractor is presented. Hopf bifurcation of the introduced n-scroll chaotic system is analytically and numerically determined. The bifurcation diagram and Lyapunov spectrum of the system are calculated and the results show that the system has a chaotic regime in a wider parameter range. Furthermore, period-3 behavior has been observed on the system. Circuit realizations of two-, three-, four-, and five-scroll chaotic attractors are also presented.     

Frequency Sensitivity of Signal Detection in Scale-Free Networks

It has been recently reported that scale-free topology favors the detection of a weak signal because of the higher amplification at the hub node than that at other nodes [Phys. Ref. I？, 78（2008）046111]. We investigate the corresponding synchronization behaviors and find that the favorite detection depends not only on the coupling and noise strengths but also on the frequency of the external signal. We reveal theoretically and numerically that the amplification effect of the hub node will decrease monotonously with the external frequency, which is useful to understand the high sensitivity of animal visual and auditory systems to weak external signals.     

Coexisting tori and torus bubbling in non-smooth systems

Pulse modulated power electronic converters represent an important class of piecewise-smooth dynamical systems with a broad range of applications in modern power supply systems. The paper presents a detailed investigation of a number of unusual bifurcation phenomena that can occur in power converters with multilevel control. In the first example a closed invariant curve arises in a border-collision bifurcation as a period-6 saddle cycle collides with a stable fixed point of focus type and transforms it into an unstable focus point. The second example involves the formation of a structure of coexisting tori through the interplay between border-collision and global bifurcations. We examine the behavior of the system in the presence of two coexisting stable resonance tori and finally show how an existing torus can develop heteroclinic bubbles that connect the points of a stable resonance cycle with an external pair of saddle and focus cycles. The appearance of these structures is explained in terms of a sequence torus-birth bifurcations with pairs of stable and unstable tori folding one over the other.     

布拉格型声光双稳系统对弱信号的放大作用研究

在分岔点附近，通过对描述布拉格（Ｂｒａｇｇ）型声光双稳系统的差分－微分方程进行线性稳定性分析，得到了系统对小信号放大时的共振频率，给出了放大倍数的表达式。然后通过数值计算模拟出系统对小信号的放大过程，结果与理论分析相符     

Analytical investigations on crosstalk in fiber Raman amplification for WDM systems

In this paper, the analytical investigations for the crosstalk in fiber amplification for WDM channels have been reported. The crosstalk between WDM channels with external Raman amplification including second-order dispersion terms has been investigated. It has been shown that the higher-order dispersion severely degrades the performance of optical communication systems. To ensure small crosstalk, the signal gain and the injected pump power should be limited to the value well below the threshold of Raman amplification. Analytical formula for signal interference ratio (SIR) and gain in fiber Raman amplifier including the impact of second-order dispersion terms for WDM systems has been derived at different wavelengths. It has also been shown that there is increase in crosstalk due to second-order dispersion.     

基于改善关联性Buck变换器的混沌控制

由于Buck变换器具有非线性特性, 在一定参数条件下, 它会处于混沌状态, 此时Buck变换器不能正常工作. 为了抑制Buck变换器的混沌现象, 本文首先建立了Buck变换器的精确状态方程模型, 然后通过分析可控范围图、开关逻辑图、相图、电感电流波形、输出电压波形, 研究了基于改善Buck变换器的电感电流与输出电压之间关联性的混沌控制策略. 研究结果表明: 该控制策略能够将处于混沌状态的Buck变换器稳定在周期1, 2, 4, 8轨道, 且该控制策略不需要预先确定期望的目标轨道, 不依赖于Buck变换器的电路参数, 只取决于一个外部参数即耦合强度, 所以该控制策略同样适用于其他 拓扑结构的功率变换器. 关键词： 混沌控制 Buck变换器 关联性 耦合强度     

The dynamics of a symmetric coupling of three modified quadratic maps

We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-l, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.     

电感电流伪连续导电模式下Buck变换器的动力学建模与分析

以电感电流伪连续导电模式(pseudo-continuous conduction mode, PCCM)下Buck变换器为例, 通过对开关变换器的开关模态的完整描述, 建立了PCCM Buck变换器的精确离散时间模型. 基于该模型, 研究了PCCM Buck变换器在负载电阻、电感等效串联电阻、电感、电容、参考电流和输入电压等电路参数变化时的分岔行为, 并揭示了变换器存在的次谐波振荡、倍周期分岔和混沌等复杂动力学行为. 基于分段光滑开关模型的数值仿真, 得到变换器在不同负载电阻下的时域波形图和相轨图, 验证了离散时间模型的正确性. 理论分析和仿真结果表明: PCCM Buck变换器更适合工作在轻载条件, 加大负载会导致变换器工作状态的失稳以及工作模式的转移; 电感的等效串联电阻对变换器稳定性具有一定程度的影响, 且等效串联电阻越大, 变换器越稳定. 研究结果对于设计与控制PCCM Buck变换器具有重要意义.     

Double resonance in star networks of bistable units with disordered signals

It has been found that a hub node is better able to amplify weak external signals than leaf nodes in star networks. But hub-enhanced amplification is only attained by a single hub node and is limited to weak coupling strength. We show here that random initial phases in external weak signals do not affect the hub-enhanced amplification at weak coupling strength. Instead, they can improve the responses of all the leaf nodes to external signals at large coupling strength,resulting in a double resonance-like signal amplification. We use a reduced model to analyze the influence of the star structure and random initial phases on the emergence of double resonance.