Noise-induced enhancement of stability in a metastable system with damping

Diversity-enhanced stability

We give compelling evidence that diversity, represented by a quenched disorder, can produce a resonant collective transition between two unsteady states in a network of coupled oscillators. The stability of a metastable state is optimized and the mean first-passage time maximized at an intermediate value of diversity. This finding shows that a system can benefit from inherent heterogeneity by allowing it to maximize the transition time from one state to another at the appropriate degree of heterogeneity.

Stochastic resonance analysis of a coupled high-speed maglev vehicle-bridge coupled system under bounded noise

Coupled oscillations typically occur in maglev vehicle-bridge coupled systems excited by bounded noise caused by guideway irregularities. The paper employed Hamilton equations to derive the corresponding canonical transformation equations and determined the critical stable regions for two kinds of resonances using the largest Lyapunov exponents. The results show that the critical stable region between the excitation amplitude and the resonant frequency ratio is a valley shape when the system has external resonance only. When considering both internal and external resonances, the critical stable region between the excitation amplitude and resonant frequency ratio presents a small saddle shape. Energy transfers from the first to the second oscillator under with both internal and extrinsic resonance. As the guideway irregularities' coefficients increase, the maximum Lyapunov exponents of the two conditions change from negative to positive, which means that the system varies from a stable state to instability.

Dynamical stability of the weakly nonharmonic propeller-shaped planar Brownian rotator

Dynamical stability is a prerequisite for control and functioning of desired nanomachines. We utilize the Caldeira-Leggett master equation to investigate dynamical stability of molecular cogwheels modeled as a rigid, propeller-shaped planar rotator. To match certain expected realistic physical situations, we consider a weakly nonharmonic external potential for the rotator. Two methods for investigating stability are used. First, we employ a quantum-mechanical counterpart of the so-called "first passage time" method. Second, we investigate time dependence of the standard deviation of the rotator for both the angle and angular momentum quantum observables. A perturbationlike procedure is introduced and implemented to provide the closed set of differential equations for the moments. Extensive analysis is performed for different combinations of the values of system parameters. The two methods are, in a sense, mutually complementary. Appropriate for the short time behavior, the first passage time exhibits a numerically relevant dependence only on the damping factor as well as on the rotator size. However, the standard deviations for both the angle and angular momentum observables exhibit strong dependence on the parameter values for both short and long time intervals. Contrary to our expectations, the time decrease of the standard deviations is found for certain parameter regimes. In addition, for certain parameter regimes nonmonotonic dependence on the rotator size is observed for the standard deviations and for the damping of the oscillation amplitude. Hence, nonfulfillment of the classical expectation that the size of the rotator can be reduced to the inertia of the rotator. In effect, the task of designing the desired protocols for the proper control of the molecular rotations becomes an optimization problem that requires further technical elaboration.

On a delay ratio-dependent predator–prey system with feedback controls and shelter for the prey

In this paper, a class of three-species multi-delay Lotka–Volterra ratio-dependent predator–prey model with feedback controls and shelter for the prey is considered. A set of easily verifiable sufficient conditions which guarantees the permanence of the system and the global attractivity of positive solution for the predator–prey system are established by developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function. Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In addition, some numerical solutions of the equations describing the system are given to show that the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator–prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system. At the same time, the influence of the delays and shelters on the dynamics behavior of the system is also considered by solving numerically the predator–prey models.

Stabilizing effect of volatility in financial markets

In financial markets, greater volatility is usually considered to be synonymous with greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To investigate this surprising feature, here we propose using the mean first hitting time, i.e., the average time a stock return takes to undergo for the first time a large negative (crashes) or positive variation (rallies), as an indicator of price stability, and relate this to a standard measure of volatility. In an empirical analysis of daily returns for 1071 stocks traded in the New York Stock Exchange, we find that this measure of stability displays nonmonotonic behavior, with a maximum, as a function of volatility. Also, we show that the statistical properties of the empirical data can be reproduced by a nonlinear Heston model. This analysis implies that, contrary to conventional wisdom, not only high, but also low volatility values can be associated with higher instability in financial markets. This proposed measure of stability can be extremely useful in risk control.

Dynamical stability of the one-dimensional rigid Brownian rotator: the role of the rotator's spatial size and shape

We investigate dynamical stability of a single propeller-like shaped molecular cogwheel modelled as the fixed-axis rigid rotator. In the realistic situations, rotation of the finite-size cogwheel is subject to the environmentally-induced Brownian-motion effect that we describe by utilizing the quantum Caldeira-Leggett master equation. Assuming the initially narrow (classical-like) standard deviations for the angle and the angular momentum of the rotator, we investigate the dynamics of the first and second moments depending on the size, i.e. on the number of blades of both the free rotator as well as of the rotator in the external harmonic field. The larger the standard deviations, the less stable (i.e. less predictable) rotation. We detect the absence of the simple and straightforward rules for utilizing the rotator's stability. Instead, a number of the size-related criteria appear whose combinations may provide the optimal rules for the rotator dynamical stability and possibly control. In the realistic situations, the quantum-mechanical corrections, albeit individually small, may effectively prove non-negligible, and also revealing subtlety of the transition from the quantum to the classical dynamics of the rotator. As to the latter, we detect a strong size-dependence of the transition to the classical dynamics beyond the quantum decoherence process.

Enhancing Metastability by Dissipation and Driving in an Asymmetric Bistable Quantum System

The stabilizing effect of quantum fluctuations on the escape process and the relaxation dynamics from a quantum metastable state are investigated. Specifically, the quantum dynamics of a multilevel bistable system coupled to a bosonic Ohmic thermal bath in strong dissipation regime is analyzed. The study is performed by a non-perturbative method based on the real-time path integral approach of the Feynman-Vernon influence functional. We consider a strongly asymmetric double well potential with and without a monochromatic external driving, and with an out-of-equilibrium initial condition. In the absence of driving we observe a nonmonotonic behavior of the escape time from the metastable region, as a function both of the system-bath coupling coefficient and the temperature. This indicates a stabilizing effect of the quantum fluctuations. In the presence of driving our findings indicate that, as the coupling coefficient γ increases, the escape time, initially controlled by the external driving, shows resonant peaks and dips, becoming frequency-independent for higher γ values. Moreover, the escape time from the metastable state displays a nonmonotonic behavior as a function of the temperature, the frequency of the driving, and the thermal-bath coupling, which indicates the presence of a quantum noise enhanced stability phenomenon. Finally, we investigate the role of different spectral densities, both in sub-Ohmic and super-Ohmic dissipation regime and for different cutoff frequencies, on the relaxation dynamics from the quantum metastable state. The results obtained indicate that, in the crossover dynamical regime characterized by damped intrawell oscillations and incoherent tunneling, the spectral properties of the thermal bath influence non-trivially the short time behavior and the time scales of the relaxation dynamics from the metastable state.

Noise-induced bistability in the fate of cancer phenotypic quasispecies: a bit-strings approach

Tumor cell populations are highly heterogeneous. Such heterogeneity, both at genotypic and phenotypic levels, is a key feature during tumorigenesis. How to investigate the impact of this heterogeneity in the dynamics of tumors cells becomes an important issue. Here we explore a stochastic model describing the competition dynamics between a pool of heterogeneous cancer cells with distinct phenotypes and healthy cells. This model is used to explore the role of demographic fluctuations on the transitions involving tumor clearance. Our results show that for large population sizes, when demographic fluctuations are negligible, there exists a sharp transition responsible for tumor cells extinction at increasing tumor cells' mutation rates. This result is consistent with a mean field model developed for the same system. The mean field model reveals only monostability scenarios, in which either the dominance of the tumor cells or the dominance of the healthy cells is found. Interestingly, the stochastic model shows that for small population sizes the monostability behavior disappears, involving the presence of noise-induced bistability. The impact of the initial populations of cells in the fate of the cell populations is investigated, as well as the transient times towards the healthy and the cancer states.

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index β, causing a stochastic bifurcation at the non-Gaussianity index value α = 1 (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value β≈-0.5 (i.e., beyond which the likelihood for transcription suddenly reversed for α values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case (β = 0). While in the multiplicative noise case, non-Gaussianity index value α = 1 is a separating point or line for both the MFET and the FEP. We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.

Stochastic resonance in a delayed triple-well potential driven by correlated noises

In this paper, we investigate stochastic resonance (SR) in a delayed triple-well potential subject to correlated noises and a harmonic signal. The stationary probability density, together with the response amplitude of the system, is obtained by using the small time delay approximation. It is found that the time delay, noise intensities, and the cross-correlation between noises can induce the occurrence of the transition. Moreover, the appropriate choice of noise intensities and time delay can improve the output of the system, enhance the SR effect, and lead to the phenomenon of noise enhanced stability. Especially, the stochastic multi-resonance phenomenon is observed when the multiplicative and additive noises are correlated. Finally, the theoretical results are well verified through numerical simulations.