Long-Time Dynamic Response and Stochastic Resonance of Subdiffusive Overdamped Bistable Fractional Fokker--Planck Systems

To explore the influence of anomalous diffusion on stochastic resonance （SR） more deeply and effectively, the method of moments is extended to subdiffusive overdamped bistable fractional Fokker-Planck systems for calculating the long-time linear dynamic response. It is found that the method of moments attains high accuracy with the truncation order N = 10, and in normal diffusion such obtained spectral amplification factor （SAF） of the first-order harmonic is also confirmed by stochastic simulation. Observing the SAF of the odd-order harmonics we find some interesting results, i.e. for smaller driving frequency the decrease of subdiffusion exponent inhibits the stochastic resonance （S.R）, while for larger driving frequency＂ the decrease of subdiffusion exponent enhances the second SR peak, but the first one vanishes and a double SR is induced in the third-order harmonic at the same time. These observations suggest that the anomalous diffusion has important influence on the bistable dynamics.     

基于Kramers逃逸速率的调参随机共振机理

根据Kramers逃逸速率的特性,阐明了随机共振信号的频率被限制在Kramers逃逸速率极限值一半的范围内,这种限制是制约大频率信号产生随机共振的原因.在进一步揭示二次采样随机共振频率尺度变换机理的基础上,证明了二次采样频率尺度可以把任意信号频率映射变换到随机共振频率尺度上的结论.相对于二次采样变换方法,由于双稳系统参数的调节很难使Kramers逃逸速率的一半达到实际信号的大频率,因此系统参数只能在随机共振的小参数频率范围内调节来实现随机共振. 关键词： 双稳随机共振 二次采样频率变换 系统参数调节 Kramers逃逸速率     

Circuit implementation and multiform intermittency in ahyper-chaotic model extended from Lorenz system

<正>This paper presents a non-autonomous hyper-chaotic system,which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system.The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits,intermittency,chaos and hyper-chaos by controlling the frequency of the periodic signal.The phenomenon has been well demonstrated by numerical simulations,bifurcation analysis and electronic circuit realization.Moreover,the system is concrete evidence for the presence of Pomeau-Manneville Type-Ⅰintermittency and crisis-induced intermittency.The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing.By statistical analysis,power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states.     

The role of soft versus hard bistable systems on stochastic resonance using average cycle energy as a quantifier

Using the input energy per cycle as a quantifier of stochastic resonance (SR), we show that SR is observed in superharmonic (hard) potentials. However, it is not observed in subharmonic (soft) potentials, even though the potential is bistable. These results are consistent with recent observations based on amplitude of average position as a quantifier. In both soft and hard potentials, we observe resonance phenomenon as a function of the driving frequency. The nature of probability distributions of average work are qualitatively different for soft and hard potentials.     

Signal detection for frequency-shift keying via short-time stochastic resonance

A series of short-time stochastic resonance (SR) phenomena, realized in a bistable receiver, can be utilized to detect a train of information represented by signals that adopt frequency-shift keying (FSK). It is demonstrated that the values of noise intensity at resonance regions are close for adjacent periodic signals with an appropriate frequency separation. This establishes the possibility of decoding subthreshold or slightly suprathreshold M-ary FSK signals in bistable receivers. Furthermore, the mechanism of FSK signal detection via short-time SR effects is elucidated in terms of the receiver response speed. This phenomenon provides a possible mechanism for information processing in a bistable device operating in nonstationary noisy environments, where even the inputs appear over a short timescale or have a frequency shift.     

Collective transport of coupled particles

We consider the dynamics for a system consisting of three coupled, driven and damped particles evolving in a symmetric and spatially-periodic potential landscape. The three coupled particles, known as a trimer, form a one-dimensional chain. Our main focus is concentrated on running solutions for this system. In particular, we explore the nature of these solutions. Therefore, proofs are derived showing that for the three coupled particles in a running state 1) each particle travels the same distance in a single period and, 2) there is only one possible transport scenario – namely when the particles travel in rod-like motion. It is also shown that in such a state, the particles, evolving on a periodic attractor, no longer exchange energy with one another. Thus in a running state the three-particle system, evolving in general in a high-dimensional phase space, effectively reduces to a single-particle system and motion takes place on a lower dimensional attractor, viz. a limit cycle. Furthermore analysis is carried out exploring how the frequency of the driving affects coherent particle transport. Numerical evidence demonstrates that there is a small window of frequencies for which (low-dimensional) limit cycles exist allowing for directed particle transport to occur.     

兴奋性自突触引起神经簇放电频率降低或增加的非线性机制

兴奋和抑制性作用分别会增强和压制神经电活动,这是神经调控的通常观念,在神经信息处理中起重要作用.本文选取了放电簇和阈下振荡相交替、放电簇谷值小于阈下振荡谷值的Homoclinic/Homoclinic型簇放电,研究发现时滞和强度合适的兴奋性自突触电流作用在放电簇的谷值附近时,能引起簇内放电个数降低,并进而导致平均放电频率降低,这是不同于通常观念的新现象.进一步,用快慢变量分离获得的分岔和相轨迹,揭示了阈下振荡和放电簇分别对应快子系统的阈下和阈上极限环,兴奋性自突触电流引起阈上极限环向阈下极限环的转迁导致放电提前结束是频率降低原因.并与近期在Fold/Homoclinic簇放电报道的兴奋性自突触诱发的簇内放电个数降低但放电频率增加的现象和机制进行了比较.研究结果丰富了神经电活动的反常现象并揭示了背后的非线性机制,给出了调控簇放电的新手段,揭示了兴奋性自突触的潜在功能.     

Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage. Supported by the National Natural Science Foundation of China (Grant No. 10532070), the Knowledge Innovation Program of Chinese Academy of Sciences (Grant No. KJCX2-YW-L07), and the LNM Initial Funding for Young Investigators     

倍频纳秒激光驱动类氖锗X射线激光的研究

利用JB19等程序分别对基频和倍频激光驱动条件下类氖锗X射线激光进行了模拟计算,结果表明利用倍频激光驱动同样也能够获得高强度的类氖锗X射线激光输出,只是对驱动激光的输出要求要高3.3倍.尽管如此,这也为将来在大型激光装置上开展类氖系列X射线激光研究指明了方向.初步的实验研究也证实了利用倍频纳秒激光驱动能够获得类氖锗X射线激光输出的结果. 关键词： X射线激光 类氖锗 数值模拟     

Localization properties of driven disordered one-dimensional systems

We generalize the definition of localization length to disordered systems driven by a time-periodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.     

Role of the driving frequency in a randomly perturbed Hodgkin-Huxley neuron with suprathreshold forcing

The present paper examines the influence of the forcing frequency on the response of a randomly perturbed Hodgkin-Huxley system in the realm of suprathreshold amplitudes. Our results show that, in the presence of noise, the choice of driving frequency can seriously affect the precision of the external information transmission. At the same level of noise the precision can either decrease or increase depending on the driving frequency. We demonstrate that the destructive influence of noise on the interspike interval can be effectively reduced. That is, with driving signals in certain frequency ranges, the system can show stable periodic spiking even for relatively large noise intensities. Here, the most accurate transmission of an external signal occurs. Outside these frequency ranges, noise of the same intensity destroys the regularity of the spike trains by suppressing the generation of some spikes. On the other hand, we show that noise can have a reconstructive role for certain driving frequencies. Here, increasing noise intensity enhances the coherence of the neuronal response.     

Optimal information transmission in nonlinear arrays through suprathreshold stochastic resonance

We examine the optimal threshold distribution in populations of noisy threshold devices. When the noise on each threshold is independent, and sufficiently large, the optimal thresholds are realized by the suprathreshold stochastic resonance effect, in which case all threshold devices are identical. This result has relevance for neural population coding, as such noisy threshold devices model the key dynamics of nerve fibres. It is also relevant to quantization and lossy source coding theory, since the model provides a form of stochastic signal quantization. Furthermore, it is shown that a bifurcation pattern appears in the optimal threshold distribution as the noise intensity increases. Fisher information is used to demonstrate that the optimal threshold distribution remains in the suprathreshold stochastic resonance configuration as the population size approaches infinity.     

A kinetic Monte Carlo study for stripe-like magnetic domains in ferrimagnetic thin films

The topology and dynamics of stripe-like magnetic domains obtained in a ferrimagnetic garnet subjected to a time-dependent external magnetic field is studied experimentally and theoretically. Experiments are performed on a commercially available magnetic bubble apparatus, allowing the observation of the time-evolution of the magnetic domain structure. The system is modeled by a meso-scale Ising-type lattice model. Exchange and dipolar interactions between the spins, and interaction of the spins with the external magnetic field are considered. The model is investigated by kinetic Monte Carlo simulations with time-varying transition rates. In the limit of low temperatures the elaborated model leads to a magnetic domain topology and dynamics that is similar to the ones observed in the experiments. In the highly non-equilibrium limit with a high driving frequency the model reproduces the experimentally recorded hysteresis loops as well.     

Memory effects on stochastic resonance

We study the phenomenon of stochastic resonance (SR) in a bistable system with internal colored noise. In this situation the system possesses time-dependent memory friction connected with noise via the fluctuation-dissipation theorem, so that in the absence of periodic driving the system approaches the thermodynamic equilibrium state. For this non-Markovian case we find that memory usually suppresses stochastic resonance. However, for a large memory time SR can be enhanced by the memory.     

Ultrasonic plastic welding using fundamental and higher resonance frequencies

Ultrasonic plastic welding using fundamental and higher resonance frequency vibrations simultaneously was studied. Using higher frequency, welding characteristics is improved due to the larger vibration loss of plastic materials. The 26 kHz welding tip vibrates in maximum velocity of over 4.5 m/s (peak-to-zero value) under a fundamental resonance frequency and there are several higher resonance frequencies up to 95 kHz whose vibration velocities are over one-third that of the fundamental frequency. Welding characteristics of 1.0-mm-thick polypropylene sheets are measured in the cases the vibration system are driven under combined driving voltages of fundamental and higher resonance frequencies. Welded area increases as number of driven higher frequencies increases. The welded area by three frequencies is about three to four times that of the case where only the fundamental frequency is driven. The welding characteristics of ultrasonic plastic welding are improved significantly by driving higher resonance frequencies simultaneously.     

Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

This paper investigates the stochastic resonance (SR) phenomenon induced by the multiplicative periodic signal in a cancer growth system with the cross-correlated noises and time delay. To describe the periodic change of the birth rate due to the periodic treatment, a multiplicative periodic signal is added to the system. Under the condition of small delay time, the analytical expression of the signal-to-noise ratio R_{\rm SNR} is derived in the adiabatic limit. By numerical calculation, the effects of the cross-correlation strength \lambda and the delay time \tau on R_{\rm SNR} are respectively discussed. The existence of a peak in the curves of R_{\rm SNR} as a function of the noise intensities indicates the occurrence of the SR phenomenon. It is found that \lambda and \tau play opposite role on the SR phenomenon, i.e., the SR is suppressed by increasing \lambda whereas it is enhanced with the increase of \tau, which is different from the case where the periodic signal is additive.     

Stochastic Resonance in a Linear Fractional Langevin Equation

The fractional Langevin equation is derived from the generalized Langevin equation driven by the additive fractional Gaussian noise. We investigate the stochastic resonance (SR) phenomenon in the underdamped linear fractional Langevin equation under the external periodic force and multiplicative symmetric dichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform technique, we obtain the exact expressions of the amplitude and signal-to-noise ratio (SNR) of the system. By studying the impacts of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude and SNR. The results indicate that the bona fide SR, conventional SR and the wide sense of SR phenomena occur in the proposed linear fractional system.