Anharmonic resonances with recursive delay feedback

We consider application of time-delayed feedback with infinite recursion for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, recursive delay feedback exhibits resonances between feedback and nonlinear harmonics, leading to a resonantly strong or weak oscillation coherence even for a small anharmonicity. Remarkably, these small-anharmonicity induced resonances can be stronger than the harmonic ones. Analytical results are confirmed numerically for van der Pol and van der Pol-Duffing oscillators.     

Delayed feedback as a means of control of noise-induced motion

Time-delayed feedback is exploited for controlling noise-induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the time scales of noise-induced motion by changing the time delay.     

Predicting optimal drive sweep rates for autoresonance in Duffing-type oscillators: A beat method using Teager-Kaiser instantaneous frequency

Sustained resonance in a linear oscillator is achievable with a drive whose constant frequency matches the resonant frequency of the oscillator. But in oscillators with nonlinear restoring forces such as the pendulum, Duffing and Duffing-Van der Pol oscillator, the resonant frequency changes as the amplitude changes, so a constant frequency drive results in a beat oscillation instead of sustained resonance. Duffing-type nonlinear oscillators can be driven into sustained resonance, called autoresonance, when the drive frequency is swept in time to match the changing resonant frequency of the oscillator. We find that near-optimal drive linear sweep rates for autoresonance can be estimated from the beat oscillation resulting from constant frequency excitation. Specifically, a least squares estimate of the Teager-Kaiser instantaneous frequency versus time for the beat response to a stationary drive provides a near-optimal estimate of the nonstationary drive linear sweep rate needed to sustain resonance in the pendulum, Duffing and Duffing-Van der Pol oscillators. We confirm these predictions with model-based numerical simulations. An advantage of the beat method of estimating optimal drive sweep rates for maximal autoresonant response is that no model is required so experimentally generated beat oscillation data can be used for systems where no model is available.     

Theoretical study of relaxation oscillation in triply resonant OPOs

The relaxation oscillation in triply resonant optical parametric oscillators (TROs) is studied theoretically. With constant pumping, the intensity noise spectra of the signal wave consist of a zero frequency and a relaxation oscillation frequency. An accurate relation between the relaxation oscillation frequency and the pump power is obtained. The square of the inherent relaxation oscillation frequency in TROs is linear in the square root of the pump power under high-power pumping. Also, the decay rate varies rapidly with low-power pumping and slowly with high-power pumping. Significantly, when there is a relaxation oscillation in the pumping, the undulation of the signal photon density in TROs also contains the relaxation oscillation frequency of the pumping besides its inherent noise. When those two frequencies are close, a resonance will appear, which should be avoided in practice. PACS 42.65.Yj; 42.65.Sf; 42.60.Rn     

太赫兹折叠波导行波管再生反馈振荡器非线性理论与模拟

行波管再生反馈振荡器是一种新型太赫兹源器件.基于560GHz折叠波导慢波结构,对此类器件的工作原理与物理模型进行分析阐述.采用非线性互作用模型对行波管再生反馈振荡器进行详细振荡过程模拟.模拟结果显示,在550—600GHz频率下可以获得稳态振荡频率,并在560GHz处获得最大单频输出功率.结果同时表明,振荡频率随电子注电压发生跳变现象,并简要分析了其产生原因.     

Logical stochastic resonance in bistable system under α-stable noise

An autonomous stochastic system with nonlinear time-delayed feedback is investigated employing the stochastic simulation method. In the autonomous stochastic system with quadratic time-delayed feedback or under positive feedback, the nonlinear delay time fails to possess the role improving the noisy state of the system. In the autonomous stochastic system with cubic time-delayed feedback and under negative feedback, the nonlinear delay time can improve the noisy state, tuning the signal output, and generating incoherence and coherence maximization. We reveal a new kind of anti-coherence and coherence resonance phenomena induced by the nonlinear time delay in the autonomous stochastic system without external periodic force, discussing further the effects of the noise strength, the control parameter, and the feedback strength on anti-coherence and coherence resonance.     

表面杂质对NO+CO/Pt(100)反应体系振荡动力学的影响

提出了一个格气模型， 探讨催化表面的惰性杂质对NO+CO/Pt(100)反应体系振荡动力学行为的影响．研究发现表面杂质较少时，反应进程中表面重构能够形成相连通的1*1相和持续的振荡行为．当表面杂质不断增加时，反应进程中1*1相只能形成许多孤立的畴，从而在1*1相形成的随机的局域振荡的空间关联被削弱，因而体系全局的持续振荡行为演变为衰减振荡行为．当表面吸附的CO和NO的扩散速率增加时，局域振荡的空间协同又得到加强，体系又呈现出持续振荡行为．     

Controlling coherence of noisy and chaotic oscillators by a linear feedback

We analyze the dynamics of a noisy limit cycle oscillator coupled to a general passive linear system. We analytically demonstrate that the phase diffusion constant, which characterizes the coherence of the oscillations, can be efficiently controlled. Theoretical analysis is performed in the framework of linear and Gaussian approximations and is supported by numerical simulations. We also demonstrate numerically the coherence control of a chaotic system.     

Theory of fluctuations in quasiharmonic oscillators

An approach is developed for analyzing fluctuation effects in quasiharmonic oscillators formed by connecting a nonlinear inertialess element to a resonator. The effect of the nonlinear element on the resonator is treated as a pulsed process. It is assumed that the effect of noise on the system destroys the coherence and changes the response parameters of the resonator to pulse effects, this, ultimately, being responsible for the amplitude and frequency fluctuations. An equation is obtained that describes the fluctuations of the oscillation period. A detailed study is made of the fluctuations of the period in an electronic oscillator due to white noise.     

非对称耦合量子阱的吸收非线性增强

基于V 形三能级模型运用密度矩阵方程推导了非对称耦合量子阱三阶光学非线性极化率. 具体分析了三阶吸收非线性效率（三阶光学非线性极化率与线性吸收系数之比）随阱间电子相干振荡频率的变化规律. 理论结果表明：三阶吸收非线性效率对阱间电子相干振荡频率相当敏感，当阱间电子相干振荡频率增大时三阶吸收非线性效率显著增强，而当阱间电子相干振荡频率为零时，这种非线性效率类似于单量子阱情况. 与单量子阱相比，对于已设计好的非对称耦合量子阱结构其突出特征表现在，其非线性吸收与色散特性可经由沿材料生长方向偏压进行控制. 据此，我们预期利用这种非对称耦合量子阱结构能设计成光通信中的光限幅器和可控克尔光开关.     

The effect of time-delayed feedback on logical stochastic resonance

We examine the possibility of obtaining logic operation in a quartic-bistable system with linear time-delayed feedback subjected to Gaussian noise. The effect of time-delayed feedback on the effective potential well is investigated, and explicit numerical stimulation is conducted to study the influence of delay time and strength of the time-delayed feedback on the responses of the system. Although the response deteriorates slightly at low values of noise intensity with time-delayed feedback and the peak correct probability decreases from 100% when the delay time is too long, the reliability of obtaining the desired logic output is enhanced in the higher noise boundary with the help of moderate time-delayed feedback. We also found that increasing the linear factor of the system can shift the optimal noise intensity to a higher level.     

Delay control of coherence resonance in type-I excitable dynamics

We consider a simple paradigmatic system of type-I excitability subject to noise and time-delayed feedback. This system is governed by a global bifurcation, namely a saddle-node bifurcation on a limit cycle. In the absence of noise, delay can induce complex dynamics including multiple stable and unstable periodic orbits. Random fluctuations result in coherence resonance in dependence on the noise strength. We show that this effect can be enhanced by delayed feedback control with suitably chosen feedback strength and time delay.     

Delay-enhanced spatiotemporal order in coupled neuronal systems

In a network of noisy neuron oscillators with time-delayed coupling, we uncover a phenomenon of delay-enhanced spatiotemporal order. We find that time delay in the coupling can dramatically enhance the temporal coherence and spatial synchrony of the noise-induced spike trains. In addition, if the delay time is tuned to nearly match the intrinsic spiking period of the neuronal network, both the coherence and the synchrony reach maximum levels, demonstrating an interesting type of resonance phenomenon with delay. Such findings are shown to be robust to the change of the noise intensity and the rewiring probability of small-world network.     

一种基于串联谐振腔的高性能光电振荡器

提出了一种利用串联谐振腔来抑制光电振荡器边模的方案. 此方案中, 在传统光电振荡器结构中加入无源微波谐振腔结构来提高滤波器的Q值. 分析了该结构的基本原理, 并与传统光电振荡器结构进行对比, 此结构能有效提高边模抑制比. 实验中产生了10 GHz的微波信号, 所测得的边模抑制比达72 dB, 单边带相位噪声为-122 dBc/Hz@10 kHz. 同时, 利用锁相技术, 振荡频率的稳定性得到了很大的改善, 在3 h内漂移小于± 4 Hz. 该方案无需增加有源器件, 保留了传统光电振荡器低相位噪声的优势, 又有效抑制了边模, 为光电振荡器的应用提供了一种新的方法.     

Coherence and stochastic resonance in threshold crossing detectors with delayed feedback

We consider the dynamical behavior of threshold systems driven by external periodic and stochastic signals and internal delayed feedback. Specifically, the effect of positive delayed feedback on the sensitivity of a threshold crossing detector (TCD) to periodic forcing embedded in noise is investigated. The system has an intrinsic ability to oscillate in the presence of positive feedback. We first show conditions under which such reverberatory behavior is enhanced by noise, which is a form of coherence resonance (CR) for this system. Further, for input signals that are subthreshold in the absence of feedback, the open-loop stochastic resonance (SR) characteristic can be sharply enhanced by positive delayed feedback. This enhancement is shown to depend on the stimulus period, and is maximal when this period is matched to an integer multiple of the delay. Reverberatory oscillations, which are particularly prominent after the offset of periodic forcing, are shown to be eliminated by a summing network of such TCDs with local delayed feedback. Theoretical analysis of the crossing rate dynamics qualitatively accounts for the existence of CR and the resonant behavior of the SR effect as a function of delay and forcing frequency.     

Enhancing the relaxation oscillation frequency of a chaotic semiconductor laser transmitter using optical dual-feedback light

A method to enhance the relaxation oscillation frequency and carrier bandwidth of a delayed feedback semiconductor laser transmitter is presented using additive optical feedback light. A formula for frequency detuning of the optical dual-feedback is developed to demonstrate that frequency detuning is added with the additive optical feedback light level. The function of the relaxation oscillation frequency of the chaotic laser is theoretically determined to show that it can be broadened by including the delay time and feedback level. Numerical results demonstrate that the bandwidth with the additive optical feedback light can be enhanced 1.7 times more than the bandwidth without it and the relaxation oscillation frequency of the chaotic laser is increased to 1.8 times more than that of the laser without it. The current can enhance the relaxation oscillation frequency and bandwidth of the transmitter more efficiently.     

Propagation of spiking regularity and double coherence resonance in feedforward networks

We investigate the propagation of spiking regularity in noisy feedforward networks (FFNs) based on FitzHugh-Nagumo neuron model systematically. It is found that noise could modulate the transmission of firing rate and spiking regularity. Noise-induced synchronization and synfire-enhanced coherence resonance are also observed when signals propagate in noisy multilayer networks. It is interesting that double coherence resonance (DCR) with the combination of synaptic input correlation and noise intensity is finally attained after the processing layer by layer in FFNs. Furthermore, inhibitory connections also play essential roles in shaping DCR phenomena. Several properties of the neuronal network such as noise intensity, correlation of synaptic inputs, and inhibitory connections can serve as control parameters in modulating both rate coding and the order of temporal coding.     

生物钟基因网络中分子噪声诱导的日夜节律振荡及相干共振

研究了果蝇细胞内生物钟基因调节网络的分子噪声，特别讨论了生物钟系统处于略微远离振荡区域的稳态时分子噪声对于时钟蛋白的日夜节律振荡的影响.结果表明：(1)虽然时钟蛋白合成或者衰减的生化反应事件是在随机的时间间隔里随机发生的，但系统可以依赖自身固有的调节机理诱导出明显的日夜节律振荡；(2)分子噪声诱导的日夜节律振荡的相干性可以在合适的分子噪声水平下到达最佳，说明了相干共振现象的发生.