基于描述函数方法的神经群自激振荡特性分析

在无外界刺激时神经群表现为节律性自激振荡,自激振荡是非线性系统特有的一种运动形式.在非线性描述函数法理论框架下,对神经群模型自激振荡特性进行分析,并揭示其产生机理.神经群模型的sigmoid非线性函数(简称为S函数)是其自激振荡的根源.首先,求解S函数的描述函数;然后,基于S函数的描述函数得到神经群模型正反馈回路S函数和负反馈回路S函数的等效增益,在此基础上将神经群模型转化为可用描述函数法分析的典型结构形式;最后,应用描述函数法理论对神经群模型自激振荡特性进行理论分析,得到自激振荡特性的定量描述,并通过仿真分析对理论分析结果进行了验证.理论分析及仿真分析结果表明基于描述函数方法的神经群自激振荡特性分析方法是正确有效的.S函数是神经系统的典型非线性环节,S函数的处理方法及神经群自激振荡特性分析方法对于其他神经模型的自激振荡特性分析具有参考价值.     

Nonlinear dynamics of breathing current filaments inn-GaAs andp-Ge

A novel model is presented for spatio-temporal pattern formation in semiconductors. It leads to self-generated nonlinear current oscillations due to “breathing” current filaments in the regime of impurity impact ionization. The four qualitatively different regimes which have been observed in Ge with increasing current are consistently explained as: a stationary nonconducting state; bulkdominated oscillations; breathing filaments; stable filaments. The physical origin of the breathing oscillations is impact ionization coupled with transverse diffusion and longitudinal dielectric relaxation. A method is developed to derive simple nonlinear dynamic equations for the filament radius and the position of the peak transverse electric field by a nonlinear mode expansion.     

Investigations on dynamics of interacting cavitation bubbles in strong acoustic fields

Given its importance to the dynamics of cavitation bubbles, the mutual interaction between bubbles was carefully investigated in this work. The cavitation noises emitted in different sonication conditions were recorded to study the dynamical behavior of the bubbles. The frequency spectra of the noises suggest that the dispersing state of the bubbles severely influence the oscillations of bubbles, and that the nonlinear feature of the dynamics of cavitation bubbles, imposed by the mutual bubble-bubble interaction, gradually develops with the decrease of the dispersing height. Theoretical analysis shows that the size difference between the interacting bubbles should be responsible for the increase of nonlinearity of the oscillation, and that the decrease of the distance between them could effectively enhance the nonlinear feature of the oscillation of the bubble, both of which agree well with the experimental observation.     

Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions.Jansen's neural mass model(NMM) was initially proposed to study the origin of alpha oscillations.Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods.In this study,we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM.First,the sigmoid nonlinear function in the NMM is approximated by its describing function,allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part.Second,by conducting a theoretical analysis,we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and,furthermore,accurately determine its amplitude and frequency.The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations.Furthermore,strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.     

Nonlinear longitudinal oscillations of relativistic plasma

The investigation has been made of nonlinear forced longitudinal oscillations of a relativistic plasma. It was demonstrated that: a) the nonlinear terms (v▽)p arising in the equations of motion do not restrict the electron oscillation amplitude increase in the region of plasma resonance; b) the nonlinear terms due to the relativistic nature of oscillations, firstly, limit the oscillation amplitude in the resonance region and, secondly, lead to the development of a parametric instability. The harmonic, sub- and ultraharmonic oscillations turned out to be unstable. The conditions for the instability as well as expressions for the growth rates of unstable oscillations were obtained.     

Low frequency oscillations in semi-insulating GaAs: a nonlinear analysis

We have observed low frequency current oscillations in a semi-insulating GaAs sample grown by low temperature molecular beam epitaxy. For this, an experimental setup proper to measure high impedance samples with small external noise was developed. Spontaneous oscillations in the current were observed for some bias conditions. Although measurements were carried out from room temperature down to liquid helium, the dynamical analysis was carried out around 200 K where the signal to noise ratio was fairly favorable. To increase the data quality we have also used a noise reduction algorithm suitably developed for nonlinear systems. We observed attractors having low embedding dimension, limit cycle bifurcations, and chaotic behavior characteristic of nonlinear dynamical processes in route to chaos. Attractor reconstruction, Poincare sections, Lyapunov exponents, and correlation dimension were also analyzed.     

一个跃变电路切换系统的振荡行为及分岔机理分析

本文研究两个非线性电路系统通过开关组成的时间切换系统的复杂振荡行为及其产生机理.利用开环运算放大器放大倍数为极大值的特性,即运算放大器总是处于正的或负的饱和状态,当输入电压从负过零变正时,输出电压从正饱和状态跃变为负饱和状态,本文选择子电路系统中的非线性部分为跃变函数.首先对两个子系统进行了稳定性分析,给出了不同参数条件下的振荡行为,然后在子系统单个参数在一定范围内变化,而其他参数保持不变的情况下,研究了切换系统的复杂振荡特征,并分析了其产生机理.由于子系统方程的非光滑性和切换带来的整个系统的非光滑性,使得整个系统的周期振荡轨迹有四个切换点,随着参数的变化,周期振荡轨线与非光滑分界面发生擦边分岔,导致周期振荡分裂成两个对称的周期振荡.并且研究了切换点位置改变对整个系统周期振荡行为的影响以及切换点处的分岔机理.     

Low-frequency current oscillations in a linear hot-cathode discharge

Low-frequency (ω ⪡ ω_pi) plasma oscillations in the transition regime between the high and the low current mode of a thermionic hot-cathode discharge are investigated experimentally. This type of current oscillation often shows chaotic dynamics. The current oscillations are related to nonlinear short wavelength potential structures which are identified as ion bunches formed by a fluctuating ionization front. These ion bunches are separated by ion holes and move at ion thermal speed rather than ion acoustic speed. By entering the negative space charge region of the cathode sheath, the ion bunches trigger electron current fluctuations that provide the required feedback mechanism for the observed wave train formation.     

行波管放大器中的电子混沌现象

用自洽方程模拟了波-粒相互作用过程中的电子混沌行为.结果表明：随着电流的增大，电子在相空间的运动轨道将变得混沌，混沌轨道受失谐量的影响.在时间上，电子混沌比场的极限环和混沌振荡出现要早.与场出现极限环振荡的电流阈值相比,出现电子混沌的电流阈值要小；在场呈极限环状态的“软”非线性区域，电子的混沌轨道占据大部分相空间；而在场混沌的“硬”非线性区域，混沌轨道则弥漫在整个相空间.当电流一定时,电子的混沌运动图样是不变的；在一定的电流范围内， 场的极限环和混沌振荡特征是确定的， 但它们的输出功率是不确定的. 关键词： 行波管放大器 电子混沌 相空间轨道 非线性相互作用     

Dipole oscillations in a Bose-Fermi mixture in the time-dependent approach

We study the dipole collective oscillations in a Bose-Fermi mixture, which are formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation, using a dynamical time-dependent approach. We find a large difference in the behavior of fermion oscillations between the time-dependent approach and the usual approaches such as the random-phase approximation. The dipole oscillation of the Bose-Fermi mixture cannot be described with simple center-of-mass motions of the two gases.     

The physics of space charge instabilities and temporal chaos in extrinsic photoconductors

This paper reviews experimental and theoretical work carried out on space charge instabilities and temporal chaotic behavior in cooled extrinsic p-type Germanium photoconductors. Measured dc current-voltage (I–V) characteristics of these devices are strongly nonlinear for moderate electric fields 0.1 V/cm due to field dependence of the rates of free hole capture and impurity impact ionization. Below the threshold field for impurity breakdown, Ge samples behave like damped nonlinear oscillators, exhibiting characteristic chaotic response when driven by a time-periodic voltage. Above impurity breakdown, we observe voltage-controlled negative differential resistance (NDR) in the I–V curves accompanied by spontaneous current oscillations due to moving space charge domains with velocities 10³ to 10⁴ cm/s. Measurements are well explained by a simple rate equation model in which negative differential behavior in the impact ionization rate plays a crucial role. Related work on semiconductor chaos and possible future directions for research are also mentioned.     

外控弱周期电流约束下电极B-Z反应体系中的时间自组织

以经典BZ化学反应体系的三变量Oregonator模型及电极过程动力学为基础,提出了外控弱周期电极电流约束下电极BZ反应体系与体相BZ反应体系相互耦合的动力学模型.在体相处于稳定定态参数条件下,系统地研究了外控弱周期电流约束下电极BZ反应体系中的动力学行为,定量分析了电流慢变流型上的准定态稳定性及有利于出现极限环振荡区域.研究表明,与以前所报道的外控弱周期电位约束情况类似,在外控弱周期电流约束下电极BZ反应体系中的极限环振荡区域亦发生了蜕变,但体系对外控电流约束中的这种持续性之周期扰动的响应表现在两个方面:有利于出现极限环振荡区域的缩变及原非振荡区胁迫振荡的出现.     

Giant oscillations of electron temperature during steady-state operation on Tore Supra

During fully noninductively driven discharges in the Tore Supra tokamak, large spontaneous oscillations of the core electron temperature (DeltaTe/Te>50%) have been observed for the first time. They occurred during the standard O regime, which is itself characterized by periodic oscillations of much smaller amplitude. The "giant" oscillations appear to involve distinct mechanisms with respect to the O regime and provide a spectacular example of the complex nonlinear interactions between energy confinement, noninductive current sources, and MHD that may occur in a tokamak plasma during steady-state operation.     

Stability change of intrinsic localized mode in finite nonlinear coupled oscillators

Intrinsic localized mode (ILM) is spatially localized and temporally periodic oscillation in nonlinear coupled oscillators. We numerically investigate the dynamical stability of ILMs in a microcantilever array, in which ILMs were experimentally observed by Sato et al. It is found that the stability change of ILMs is due to the ratio in nonlinear potentials. This phenomenon also occurs in the array without harmonic potentials. Consequently, the stability of ILMs substantially depends on the ratio in nonlinear on-site and inter-site potentials.     

Electron-beam induced instability during filamentary current transport inn-GaAs

We report experimental investigations on the current transport ofn-GaAs under the conditions of impact ionization avalanche breakdown at low temperatures. The spontaneous formation of a single current filament was observed by means of low-temperature scanning electron microscopy. An electron-beam induced instability occurs at the onset of filamentation. We demonstrate this instability to be due to the local disturbance at the boundaries of the current filament. Our results are compared to the similar behavior ofn-GaAs under IR irradiation (firing wave instability).     

Spatially resolved observation of current filament dynamics in semiconductors

Two-dimensional imaging of the nucleation and the dynamics of current filaments generated in homogeneous p-doped germanium at 4.2 K during impurity impact ionization induced avalanche breakdown has been performed. The images were obtained by scanning the specimen surface with an electron beam and by recording the beam-induced current change in the voltage-biased samples. This new method is expected to identify in particular the filament configurations showing chaotic temporal resistance behavior.     

Observation of reflex klystron oscillation phenomena in a plasma

Reflex klystron electron oscillation, occurring in a plasma potential well formed in a system consisting of plasma and two electrodes (filaments and a mesh grid which is at floating potential), was observed in a very simple device with only filaments and a mesh grid. This oscillation mechanism consists of three elements: 1) an acceleration region on the side in which filaments are located, which accelerates primary electron beams emitted from filaments; 2) a deceleration region on the side in which the mesh grid is located, which causes the reflection of the beams; and 3) a plasma region. In addition, the velocity modulation of primary electron beams is given by the electron plasma oscillation at the presheath on the filament side. The maximum amplitude and frequency of an oscillation obtained by this mechanism were V_pp=210 mV 210 mV and f=200 MHz, respectively. These values can be controlled by the discharge potential     

Subharmonic excitation of the eigenmodes of charged particles in a Penning trap

When parametrically excited, a harmonic system reveals a nonlinear dynamical behaviour which is common to non-deterministic phenomena. The ion motion in a Penning trap -- which can be regarded as a system of harmonic oscillators -- offers the possibility to study anharmonic characteristics when perturbed by an external periodical driving force. In our experiment we excited an electron cloud stored in a Penning trap by applying an additional quadrupole r.f. field to the endcaps. We observed phenomena such as individual and center-of-mass oscillations of an electron cloud and fractional frequencies, so-called subharmonics, to the axial oscillation. The latter show a characteristic threshold behaviour. This phenomenon can be explained with the existence of a damping mechanism affecting the electron cloud; a minimum value of the excitation amplitude is required to overcome the damping. We could theoretically explain the observed phenomenon by numerically calculating the solutions of the damped differential Mathieu equation. This numerical analysis accounts for the fact that for a weak damping of the harmonic system we observed an even-odd-staggering of the the different orders of the subharmonics in the axial excitation spectrum.Received: 22 September 2003, Published online: 2 December 2003PACS: 52.27.Jt Nonneutral plasmas - 82.80.Qx Ion cyclotron resonance mass spectrometry     

Nonlinear hydrodynamic and thermoacoustic oscillations of a bluff-body stabilised turbulent premixed flame

Turbulent premixed flames often experience thermoacoustic instabilities when the combustion heat release rate is in phase with acoustic pressure fluctuations. Linear methods often assume a priori that oscillations are periodic and occur at a dominant frequency with a fixed amplitude. Such assumptions are not made when using nonlinear analysis. When an oscillation is fully saturated, nonlinear analysis can serve as a useful avenue to reveal flame behaviour far more elaborate than period-one limit cycles, including quasi-periodicity and chaos in hydrodynamically or thermoacoustically self-excited system. In this paper, the behaviour of a bluff-body stabilised turbulent premixed propane/air flame in a model jet-engine afterburner configuration is investigated using computational fluid dynamics. For the frequencies of interest in this investigation, an unsteady Reynolds-averaged Navier–Stokes approach is found to be appropriate. Combustion is represented using a modified laminar flamelet approach with an algebraic closure for the flame surface density. The results are validated by comparison with existing experimental data and with large eddy simulation, and the observed self-excited oscillations in pressure and heat release are studied using methods derived from dynamical systems theory. A systematic analysis is carried out by increasing the equivalence ratio of the reactant stream supplied to the premixed flame. A strong variation in the global flame structure is observed. The flame exhibits a self-excited hydrodynamic oscillation at low equivalence ratios, becomes steady as the equivalence ratio is increased to intermediate values, and again exhibits a self-excited thermoacoustic oscillation at higher equivalence ratios. Rich nonlinear behaviour is observed and the investigation demonstrates that turbulent premixed flames can exhibit complex dynamical behaviour including quasiperiodicity, limit cycles and period-two limit cycles due to the interactions of various physical mechanisms. This has implications in selecting the operating conditions for such flames and for devising proper control strategies for the avoidance of thermoacoustic instability.     

基于一阶广义忆阻器的文氏桥混沌振荡器研究

通过在文氏桥振荡器中引入广义忆阻器和LC吸收网络,提出了一种忆阻文氏桥混沌振荡器.建立了忆阻文氏桥混沌振荡器的动力学模型,研究了它的平衡点和稳定性,进一步开展了电路元件参数变化时的动力学行为分析.研究发现,忆阻文氏桥混沌振荡器有3个确定的平衡点,其稳定性取决于电路元件参数,当参数发生变化时,存在周期振荡、混沌振荡、快慢效应等复杂的非线性现象.实验电路简单易制作,实验波形和数值仿真一致,较好地验证了理论分析结果.