We study theoretically a bistable systems with time-delayed feedback driven by weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the adiabatic approximation, the signal-to-noise ratio (SNR) of the system with a weak periodic force is obtained. The time-delayed feedback modulates the magnitude of SNR by changing the shape of the potential and the effective strength of signal. The maximum of SNR decreases with increasing the feedback intensity $ε$. When $ε$ is negative (or positive), the time delay can suppress (or promote) the stochastic resonance phenomenon.
The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker-Planck equation describing the system dynamics, together with the corresponding Ito-Langevin equation, are formulated. In the linear-response regime analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived…
The thermodynamics of stochastic non-Markovian systems is still widely unexplored. We present an analytical approach for the net steady-state heat flux in nonlinear overdamped systems subject to a continuous feedback force with a discrete time delay. We show that the feedback inevitably leads to a finite heat flow even for vanishingly small delay times. Application to an exemplary (bistable) system reveals that the feedback induces heating as well as cooling regimes and leads to a maximum of the medium entropy production at coherence resonance conditions.
We study the number of periodic solutions in two first order non-autonomous differential equations both of which have been used to describe, among other things, the mean magnetization of an Ising magnet in the time-varying external magnetic field. When the strength of the external field is varied, the set of periodic solutions undergoes a bifurcation in both equations. We prove that despite profound similarities between the equations, the character of the bifurcation can be very different. This results in a different number of coexisting stable periodic solutions in the vicinity of the bifurca…
Stochastic Resonance in Periodic Potentials Revisited
随机共振（SR）现象已在双稳态势中得到证实。然而，在正弦电位SR最近才被数值显示发生在磁滞回线面积方面。我们表明，SR的发生是不是特定的正弦电位，可以发生在周期性的正弦电位，$U(x)=2/3(\cos x +\cos 2x)$，以及。我们进一步表明，SR甚至可以发生在搓衣板电位，磁滞回线通常不会关闭，因为平均漂移的颗粒。在校正漂移项时，闭合的磁滞回线面积（输入能量损失）示出了通常的SR峰化行为，以及在高驱动频率范围内的有限域中的信噪比。SR的发生归因于在驱动的周期正弦和周期正弦势中有效地存在两个动力学状态。当周期势倾斜一个小的恒定斜率时，同样的解释也成立。
In this article we study transitions from low-density states towards high-density states in bistable plasma-condensate systems. We take into account an anisotropy in transference of adatoms between neighbour layers induced by the electric field near substrate. We derive the generalized one-layer model by assuming that the strength of the electric field is subjected to both periodic oscillations and multiplicative fluctuations. By studying the homogeneous system we discuss the corresponding mean passage time. In the limit of weak fluctuations, we show the optimization of the mean passage time w…
Experimental evidence of an absorbing phase transition, so far associated with spatio-temporal dynamics is provided in a purely temporal optical system. A bistable semiconductor laser, with long-delayed opto-electronic feedback and multiplicative noise shows the peculiar features of a critical phenomenon belonging to the directed percolation universality class. The numerical study of a simple, effective model provides accurate estimates of the transition critical exponents, in agreement with both theory and our experiment. This result pushes forward an hard equivalence of non-trivial stochasti…
We study a dynamical phase transition in optical bistable systems subject to a time-periodic driving field. The phase transition occurs in the structure of limit cycle as a function of the frequency of the driving field. In the thermodynamic limit, a single limit cycle is divided into two separated limit cycles at the transition point. In finite-size systems, however, there is always a single limit cycle due to the quantum tunneling effect. We use a Floquet dissipative map, which is a time-evolution operator over one period in a dynamics given by a quantum master equation, and discuss the deca…
We consider a massive particle driven with a constant force in a periodic potential and subjected to a dissipative friction. As a function of the drive and damping, the phase diagram of this paradigmatic model is well known to present a pinned, a sliding, and a bistable regime separated by three distinct bifurcation lines. In physical terms, the average velocity $v$ of the particle is nonzero only if either (i) the driving force is large enough to remove any stable point, forcing the particle to slide, or (ii) there are local minima but the damping is small enough, below a critical damping, fo…
For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time PDF, and represents, in fact, only the first member of an infinite hierarchy. We here introduce a new approach to obtain a Fokker-Planck description by using a Markovian embedding technique and a subsequent limiting procedure. On this way, we find a closed, complete FPE in an infinite-dimensional space, from which one can derive a hierarchy of FPEs. While th…
Deterministic cascade coarsening in a Bistable Gene Toggle model
Seth Kesarimal Porwal College, Rashtrasant Tukadoji Maharaj Nagpur University（塞斯·凯萨里马尔·波尔瓦尔学院，拉斯特拉桑特·图卡多吉·马哈拉杰纳格浦尔大学）；RJ College of Arts, Science and Commerce（RJ文理商学院）
