双稳杜芬振子的随机共振及其动力学机制

把矩方法应用于高斯白噪声和弱周期信号驱动的双稳杜芬振子,发现矩方法的收敛快慢与阻尼系数的大小有关,即在固定非线性参数的前提下,阻尼系数越大,收敛速度越快。在阻尼系数较大的情形,对于不同频率的弱周期输入信号,系统输出功率谱增益因子的演化防噪声强度呈单峰或双峰结构,亦即对于不同的激励频率,系统可表现出单峰或者重峰随机共振结构。为了解释这些共振结构,通过考察由波动谱密度定义的非零频率峰对噪声强度依赖性,发现重峰随机共振的发生在于噪声一方面抑制了井内运动,另一方面诱发了势垒上振动。研究结果为已有结论的修正,在统计力学等方面具有显著意义。     

Stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise

Nonlinear Dynamics - In this paper, the moment Lyapunov exponent and stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise is investigated. Firstly, the...     

Stochastic resonance in coupled weakly-damped bistable oscillators subjected to additive and multiplicative noises

With coupled weakly-damped periodically driven bistable oscillators subjected to additive and multiplicative noises under concern,the objective of this paper is to check to what extent the resonant point predicted by the Gaussian distribution assumption can approximate the simulated one.The investigation based on the dynamical mean-field approximation and the direct simulation demonstrates that the predicted resonant point and the simulated one are basically coincident for the case of pure additive noise,but for the case including multiplicative noise the situation becomes somewhat complex.Specifically speaking,when stochastic resonance(SR) is observed by changing the additive noise intensity,the predicted resonant point is lower than the simulated one;nevertheless,when SR is observed by changing the multiplicative noise intensity,the predicted resonant point is higher than the simulated one.Our observations imply that the Gaussian distribution assumption can not exactly describe the actual situation,but it is useful to some extent in predicting the low-frequency stochastic resonance of the coupled weakly-damped bistable oscillator.     

Stochastic resonance in a harmonic oscillator with damping trichotomous noise

In this paper, the phenomenon of stochastic resonance (SR) in a prototype fluctuating damping harmonic oscillator with trichotomous Markovian noise is investigated. The exact expression of output amplitude gain has been calculated using the well-known Shapiro–Loginov formula. The phenomenon of SR has been found in a broad sense—that is, the non-monotonic behavior of output amplitude gain as a function of noise parameters. Then the influences of noise amplitude, noise switching rate, and noise flatness on the output amplitude gain have also been discussed. Finally, the reverse resonance phenomenon has been presented.     

Noise effect on the signal transmission in an underdamped fractional coupled system

Nonlinear Dynamics - The signal transmission phenomenon in an underdamped fractional system composed of two harmonically coupled particles, but only the first particle, which is driven by a...     

Probabilistic response and analysis for a vibro-impact system driven by real noise

Nonlinear Dynamics - In this paper, a new stochastic averaging method is proposed to derive the stationary probabilistic response of vibro-impact system subject to real noise excitation, and the...     

Trichotomous noise induced stochastic resonance in a linear system

We investigate stochastic resonance in an underdamped linear system subjected to multiplicative trichotomous noise. We carry out the Shapiro?CLoginov formula to find the exact expression of output amplitude gain, and the impacts of the input signal frequency and noise parameters will be observed, such as noise switching rate or noise correlation time, noise amplitude and noise flatness. Then one can find the stochastic resonance for the proposed linear system.     

The Lyapunov exponent for a codimension two bifurcation system that is driven by a real noise

For a co-dimension two bifurcation system on a three-dimensional central manifold, which is parametrically excited by a real noise, a model of enhanced generality is developed in the present paper by assuming the real noise to be a component of the output of a linear filter system—a zero-mean stationary Gaussian diffusion vectoral process, which conforms with the detailed balance condition. The strong mixing condition is removed in the present paper. To handle the complexities encountered in the present work, an asymptotic analysis approach and the eigenfunction expansion of the solution to the relevant FPK equation are employed in the construction of the asymptotic expansions of the invariant measure and the maximal Lyapunov exponents for the relevant system.     

On simulation of a bistable system with fractional damping in the presence of stochastic coherence resonance

A bistable dynamical system with the Duffing potential, fractional damping, and random excitation has been modelled. To excite the system, we used a stochastic force defined by Wiener random process of Gaussian distribution. As expected, stochastic resonance appeared for sufficiently high noise intensity. We estimated the critical value of the noise level as a function of derivative order \(q\) . For smaller order \(q\) , damping enhancement was reported.     

Moment Lyapunov exponent and stochastic stability for a binary airfoil driven by an ergodic real noise

This paper presents a new method, through which the pth moment stability of a binary airfoil subjected to an ergodic real noise is obtained. The excitation included is assumed to be an integrable function of an n-dimensional Ornatein–Uhlenbeck vector process that is the output of a linear filter system and for which the strong mixing condition and the delicate balance condition are removed in the present study. By using a perturbation method and the spectrum representations of both the Fokker–Planck operator and its adjoint operator of the linear filter system, the asymptotic expressions of the pth moment Lyapunov exponent are obtained, and the results of which match the numerical results.     

Stochastic bifurcation in duffing system subject to harmonic excitation and in presence of random noise

A global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph. It is found that for this dissipative system there exists a steady state random cell flow restricted within a pipe-like manifold, the section of which forms one or two stable sets on the Poincare cell map. These stable sets are called stochastic attractors (stochastic nodes), each of which owns its attractive basin. Attractive basins are separated by a stochastic boundary, on which a stochastic saddle is located. Hence, in topological sense stochastic bifurcation can be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value. Through numerical simulations the evolution of the Poincare cell maps of the random flow against the variation of noise intensity is explored systematically. Our study reveals that as a powerful tool for global analysis, the generalized cell mapping method using digraph is applicable not only to deterministic bifurcation, but also to stochastic bifurcation as well. By this global analysis the mechanism of development, occurrence, and evolution of stochastic bifurcation can be explored clearly and vividly.     

Spiking activities in chain neural network driven by channel noise with field coupling

Nonlinear Dynamics - The distribution of electromagnetic field in both intracellular and extracellular environments can be changed by fluctuations in the membrane potential, and the effects of...     

Effects of non-Gaussian noise on logical stochastic resonance in a triple-well potential system

In this paper, we have investigated the phenomenon of logical stochastic resonance in a trip-well potential system driven by a colored non-Gaussian noise. The effects of a non-Gaussian noise on logical stochastic resonance have been discussed, and we have found that the reliability of the logic operation is dependent on the parameter q that indicates the departure from Gaussianity. The reliable region in the parameter plane of correlation time τ and noise strength D appears and expands with the decrease of q. Furthermore, it has been found that the reliable region in the plane (q,D) expands with the increase of noise color. The phenomenon can be explained successfully by the approach of Fokker–Planck equation.     

Detecting the weak high-frequency character signal by vibrational resonance in the Duffing oscillator

Nonlinear Dynamics - The weak high-frequency character signal (HCS) cannot be detected substantially by the traditional vibrational resonance (VR) theory. In this paper, by introducing the scale...     

Occurrence of gradual resonance in a finite-length granular chain driven by harmonic vibration

This study presents numerical simulations of the resonance of a finite-length granular chain of dissipative grains driven by a harmonically vibrated tube. Multiple gradual resonant modes, namely non-resonance mode, partial-resonance mode, and complete-resonance mode, are identified. With a fixed vibration frequency, increasing vibration acceleration leads to a one-one-one increase in the number of grains participating in resonance, which is equal to the number of grain-wall collisions in a vibration period. Compared with the characteristic time of the grain–grain and the grain–wall collisions, the time of free flight plays a dominant role in grain motion. This situation results in the occurrence of large opening separation gaps between the grains and independent grain–grain and grain–wall collisions. A general master equation that describes the dependence of the system energy on the length of the granular chain and the number of grain–wall collisions is established, and it is in good agreement with the simulation results. We observe a gradual step-jump increase in system energy when the vibration acceleration is continuously increased, which is dedicated to an individual energy injection. The phase diagrams in the spaces of packing density and vibration acceleration, chain length and vibration acceleration show that shorter granular chain and larger packing density favor the occurrence of complete-resonance mode.

     

Simulation and experimental studies of a vibro-impact capsule system driven by an external magnetic field

This paper studies the electromagnetic field used for driving a vibro-impact capsule prototype for small bowel endoscopy. Mathematical models of the electromagnetic field and the capsule system are introduced, and analytical solution of the magnetic force applied on the capsule is derived and verified by experiment. The impact force between the inner mass of the capsule and the capsule body is also compared via numerical simulation and experimental testing. By comparing the capsule’s progressions under different control parameters (e.g. the excitation frequency and duty cycle), the merits of using the vibro-impact propulsion are revealed. Based on the experimental results, the optimised speed of the prototype can achieve up to 3.85 mm/s. It is therefore that the potential feasibility of using the external electromagnetic field for propelling the vibro-impact capsule system is validated.

     

Transient mixed convection in an enclosure driven by a sliding lid

Transient convection of an incompressible viscous fluid in a square cavity is investigated. The temperature at the top lid is higher than that at the bottom wall, producing a stably stratified overall configuration. The vertical sidewalls are insulated. Flow is initiated by an impulsive start of the sliding motion of the top lid. The transient features of the mixed convection are delineated by procuring numerical solutions in a wide range of parameters, i.e., 400≤Re≤4,000, 1.6×10⁵≤Gr≤1.6×10⁷. Flows and heat transfer characteristics are described both in the interior core and boundary-layer regions. In the large-time limit, the steady state features are depicted. Parallel experimental efforts are made by employing the particle image velocimetry (PIV) to visualize the steady state flow and thermal fields, together with thermocouple measurements.