Huiqing Zhang

Lévy noise induced switch in the gene transcriptional regulatory system

The study of random fluctuations in a gene transcriptional regulatory system is extended to the case of non-Gaussian Lévy noise, which can describe unpredictable jump changes of the random environment. The stationary probability densities are given to explore the key roles of Lévy noise in a gene transcriptional regulatory system. The results demonstrate that the parameters of Lévy noise, including noise intensity, stability index, and skewness parameter, can induce switches between distinct gene-expression states. A further concern is the switching time (from the high concentration state to the low concentration one or from the low concentration state to the high concentration one), which is a random variable and often referred to as the mean first passage time. The effects of Lévy noise on expression and degradation time are studied by computing the mean first passage time in two directions and a number of different peculiarities of non-Gaussian Lévy noise compared with Gaussian noise are observed.

Lévy noise-induced stochastic resonance in a bistable system

AbstractThe stochastic resonance phenomenon induced by Lévy noise in a second-order and under-damped bistable system is investigated. The signal-to-noise ratio for different parameters is computed by an efficient numerical scheme. The influences of the intensity and stability index of Lévy noise, as well as the amplitude of external signal on the occurrence of stochastic resonance phenomenon are characterized. The results imply that higher signal amplitude not only enhances the output power spectrum of system but also promotes stochastic resonance, and a proper adjustment of noise intensity in a certain range enlarges the peak value of output power spectrum which is significant for stochastic resonance. Moreover, with an appropriate damping parameter, lowering the stability index leads to larger fluctuations of Lévy noise, and further weakens the occurrence of the stochastic resonance.

Parallel logic gates in synthetic gene networks induced by non-Gaussian noise.

The recent idea of logical stochastic resonance is verified in synthetic gene networks induced by non-Gaussian noise. We realize the switching between two kinds of logic gates under optimal moderate noise intensity by varying two different tunable parameters in a single gene network. Furthermore, in order to obtain more logic operations, thus providing additional information processing capacity, we obtain in a two-dimensional toggle switch model two complementary logic gates and realize the transformation between two logic gates via the methods of changing different parameters. These simulated results contribute to improve the computational power and functionality of the networks.

CHAOS IN DIFFUSIONLESS LORENZ SYSTEM WITH A FRACTIONAL ORDER AND ITS CONTROL

This paper aims to investigate the phenomenon of Diffusionless Lorenz system with fractional-order. We discuss the stability of equilibrium points of the fractional-order system theoretically, and analyze the chaotic behaviors and typical bifurcations numerically. We find rich dynamics in fractional-order Diffusionless Lorenz system with appropriate fractional order and system parameters. Besides, the control problem of fractional-order Diffusionless Lorenz system is examined using feedback control technique, and simulation results show the effectiveness of the method.

The Availability of Logical Operation Induced by Dichotomous Noise for a Nonlinear Bistable System

Instead of a continuous system driven by Gaussian white noise, logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise, which shows a phenomenon different from Gaussian white noise. We can realize two parallel logical operations by simply adjusting the values of these two thresholds. Besides, to quantify the reliability of obtaining the correct logic output, we numerically calculate the success probability, and effects of dichotomous noise on the success probability are observed, these observations show that the reliability of realizing logical operation in the bistable system can be improved through optimizing parameters of dichotomous noise.

Logical stochastic resonance in triple-well potential systems driven by colored noise

In this work, the logic stochastic resonance (LSR) phenomenon in a class of stochastic triple-well potential systems is investigated. Approximate Fokker-Planck equation is first obtained by using decoupling approximation. Then, we show that LSR can be successfully induced by additive or multiplicative Gaussian colored noise in some cases. In the absence of internal noise, LSR implementation seems impossible for a = 0 (The parameter a characterizes the depth of the potential well) since the two side wells are so deep that the particle cannot hop over the barrier into the middle well when the input signal is 0. With the increasing of a, the optimal noise band to yield flexible logic gates appears and moves to higher level of noise as the correlation time of noise increases. Compared with the Gaussian white noise, the reliable region in the parameter plane of potential depth parameter a and additive noise strength D first expands and then shrinks with increasing noise color. Furthermore, the effects of multiplicative Gaussian colored noise on LSR are investigated. It was found that the flexible and reliable logic behavior can be yielded for a = 0 due to the fact that the multiplicative Gaussian colored noise strongly affects the shape of the potential function. With the increasing of a, i.e., a = 0.25, multiplicative Gaussian white noise cannot yield desired logic behavior. Fortunately, LSR can also be expected by adjusting the correlation time of Gaussian colored noise. It can also be observed that the reliable region in the parameter plane of potential depth parameter a and multiplicative noise strength Q is small for the case of Gaussian white noise and it becomes larger with the increasing of noise color.

STOCHASTIC RESONANCE IN A BISTABLE SYSTEM DRIVEN BY WEAK PERIODIC SIGNAL WITH MULTIPLE DELAYS

The phenomenon of stochastic resonance in a bistable system with multiple delays is investigated. The analytic expression of approximation stationary probability density is obtained by using small delay approximation based on probability density approach. Numerical simulation is performed and it is shown that the analytic results are in good agreement with Monte Carlo simulation. Then the expression of the signal-to-noise (SNR) is derived by using two-state theory. Finally, the effect of multiple delays on SNR is discussed. It is found that the stochastic resonance phenomenon can be suppressed or promoted when multiple delays are increased.

Parameter-induced stochastic resonance for multiplicative three-state Markovian noise in a linear system with modulated signal

Through the nonmonotonicity of the amplitude of the periodic response, the parameter-induced stochastic resonance of the linear system modulated by bias signal for the multiplicative three-state Markovian noise is researched. We obtain the exact expression of the periodic response of the system. Then the nonmonotonic dependence of the amplitude of the periodic response on the parameters of the asymmetry degree, the switching rate and the value states of the three-state Markovian noise is analyzed. It is shown that, in some circumstances, the parameters of the three-state Markovian noise can induce the stochastic resonance in a linear system modulated by bias signal.

Stochastic resonance in a linear system induced by multiplicative asymmetric trichotomous noise

The phenomenon of stochastic resonance (SR) in a linear system with an external periodic signal derived by a multiplicative asymmetric trichotomous noise is investigated. The exact expression of the first moment has been derived by the Shapiro-Loginov formula. The non-monotonic dependence of the output amplitude of the periodic response on the asymmetric trichotomous noise parameter is presented such as the noise strength and the asymmetry degree, and the stochastic resonance phenomena are analyzed. It is found that the multiplicative asymmetric trichotomous noise can induce the SR in a linear system under some conditions in a broad sense.

Steady State Analysis of Stochastic Systems with Multiple Time Delays

In this paper, attention is focused on the steady state analysis of a class of nonlinear dynamic systems with multi-delayed feedbacks driven by multiplicative correlated Gaussian white noises. The Fokker-Planck equations for delayed variables are at first derived by Novikov’s theorem. Then, under small delay assumption, the approximate stationary solutions are obtained by the probability density approach. As a special case, the effects of multidelay feedbacks and the correlated additive and multiplicative Gaussian white noises on the response of a bistable system are considered. It is shown that the obtained analytical results are in good agreement with experimental results in Monte Carlo simulations.