Coherence versus reliability of stochastic oscillators with delayed feedback

Pitchfork and Hopf bifurcation threshold in stochastic equations with delayed feedback

The bifurcation diagram of a model nonlinear Langevin equation with delayed feedback is obtained numerically. We observe both direct and oscillatory bifurcations in different ranges of model parameters. Below threshold, the stationary distribution function p(x) is a delta function at the trivial state x=0. Above threshold, p(x) ~ x^alpha at small x, with alpha = -1 at threshold, and monotonously increasing with the value of the control parameter above threshold. Unlike the case without delayed feedback, the bifurcation threshold is shifted by fluctuations by an amount that scales linearly with…

Noise-induced standing waves in oscillatory systems with time-delayed feedback

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatio-temporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatio-temporal correlations become stronger, such that even small …

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 timescales of noise-induced motion by changing the time delay.

Dynamics of an Ensemble of Noisy Bistable Elements with Global Time-Delayed Coupling

The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates multi-stability. That is, for a strong enough positive feedback it exhibits a non-zero stationary mean field and a variety of stable oscillatory mean field states are accessible for positive and negative feedback. The regularity of the oscillatory states is maximal for a certain noise level, i.e., the system demonstrates coherence resonance. While away from…

Stochastic thermodynamics of Langevin systems under time-delayed feedback control: II. Nonequilibrium steady-state fluctuations

This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like inequalities that provide bounds to the average extracted work. Here we study stochastic fluctuations of time-integrated observables such as the heat exchanged with the environment, the extracted work, or the (apparent) entropy production. We use a path-integral formalism and focus on the long-time behavior in the stationary cooling regime, stressing the role of rare e…

含时滞耦合的Kuramoto振子系统中的高阶相互作用涌现

Emergence of higher-order interactions in systems of coupled Kuramoto oscillators with time delay

通过展开时滞成对耦合至二阶，推导出包含两体和三体相互作用的无时滞Kuramoto模型，数值模拟和稳定性分析表明两者在适当条件下同步转变定性一致，时滞导致的双稳性可由三体相互作用解释。

Cooperative Dynamics in a Network of Stochastic Elements with Delayed Feedback

Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian approximation as well as (2) a dichotomous model. The system demonstrates ordering phase transitions and multi-stability. That is, for a strong enough feedback it exhibits nontrivial stationary states and oscillatory states whose frequencies depend only on the mean of the time delay distribution function. Other observed dynamical phenomena include coherence resonance a…

Exact solution of a stochastic protein dynamics model with delayed degradation

We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained differ from others intuitively proposed and that oscillatory behavior is not possible in this system. We discuss the calculation of correlation functions in stochastic systems with delay, stressing the differences with Markovian processes. The exact results allow to clarify the interplay between stochasticity and delay.

Work statistics in the periodically driven quartic oscillator: classical versus quantum dynamics

In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external force with slowly varying amplitude both classically and within the framework of quantum mechanics. The energy change of the oscillator induced by the driving is closely related to the probability distribution of work for the system. With the amplitude $λ(t)$ of the drive increasing from zero to a maximum $λ_{max}$ and then going back to zero again initial and …

通过周期性轮询机制的噪声选民模型中的延迟交互

Delayed interactions in the noisy voter model through the periodic polling mechanism

本文研究了通过周期性轮询机制引入延迟交互对噪声选民模型平稳分布的影响，发现随轮询周期增加会出现非单调的形状参数缩放及振荡行为，但模型仍收敛于类似Beta-二项分布的平稳分布。

活性浴中的时滞杜芬（Duffing）振子

Time-delayed Duffing oscillator in an active bath

本研究探究了受高斯白噪声和Ornstein-Uhlenbeck噪声作用的受迫时滞Duffing振子的非线性动力学，揭示了噪声、驱动力与时滞的相互作用对振荡特性的调控规律，还发现足够强度的噪声和驱动可通过随机共振促进近似周期的阱间运动。