Yan-Mei Kang

Mean First Passage Time and Stochastic Resonance in a Transcriptional Regulatory System with Non-Gaussian Noise

The mean first passage time (MFPT) in a phenomenological gene transcriptional regulatory model with non-Gaussian noise is analytically investigated based on the singular perturbation technique. The effect of the non-Gaussian noise on the phenomenon of stochastic resonance (SR) is then disclosed based on a new combination of adiabatic elimination and linear response approximation. Compared with the results in the Gaussian noise case, it is found that bounded non-Gaussian noise inhibits the transition between different concentrations of protein, while heavy-tailed non-Gaussian noise accelerates the transition. It is also found that the optimal noise intensity for SR in the heavy-tailed noise case is smaller, while the optimal noise intensity in the bounded noise case is larger. These observations can be explained by the heavy-tailed noise easing random transitions.

Dynamics of a Stochastic SIS Epidemic Model with Saturated Incidence

We introduce stochasticity into the SIS model with saturated incidence. The existence and uniqueness of the positive solution are proved by employing the Lyapunov analysis method. Then, we carry out a detailed analysis on both its almost sure exponential stability and its pth moment exponential stability, which indicates that the pth moment exponential stability implies the almost sure exponential stability. Additionally, the results show that the conditions for the disease to become extinct are much weaker than those in the corresponding deterministic model. The conditions for the persistence in the mean and the existence of a stationary distribution are also established. Finally, we derive the expressions for the mean and variance of the stationary distribution. Compared with the corresponding deterministic model, the threshold value for the disease to die out is affected by the half saturation constant. That is, increasing the saturation effect can reduce the disease transmission. Computer simulations are presented to illustrate our theoretical results.

Linear response characteristics in time-dependent subdiffusive fractional Fokker–Planck equations

For the time-dependent fractional Fokker–Planck equations (FFPE), obtained from the time-independent FFPE by directly replacing the time-independent external force with a time-modulated one, we investigate its response characteristics within linear response range based on a viewpoint of global perturbation. Two general response formulas are derived in time domain and frequency domain for the subdiffusive process, and they can be reduced to the counterparts in normal diffusion when the diffusion exponent tends to 1. For two concrete examples, a Kramers–Kronig relation is also discussed and is found to have different meaning in both cases. We suggest the results may be important in exploring the phenomenon of stochastic resonance and calculating the spectral density of fluctuations.

Application of Gaussian moment method to a gene autoregulation model of rational vector field

We take a lambda expression autoregulation model driven by multiplicative and additive noises as example to extend the Gaussian moment method from nonlinear stochastic systems of polynomial vector field to noisy biochemical systems of rational polynomial vector field. As a direct application of the extended method, we also disclose the phenomenon of stochastic resonance. It is found that the transcription rate can inhibit the stochastic resonant effect, but the degradation rate may enhance the phenomenon. These observations should be helpful in understanding the functional role of noise in gene autoregulation.

Linear response characteristics of time-dependent time fractional Fokker–Planck equation systems

The time fractional Fokker?Planck equation approach is an important tool for modeling subdiffusion. When the external field is time modulated, two types of time-dependent time fractional Fokker?Planck equations have been proposed, both reduced to the same time-dependent time fractional Fokker?Planck equation when the external field is time uncorrelated. The first type is strictly deduced as the continuous limit of the continuous time random walk with time modulated Boltzmann jumping weight, while the second type is derived by ideally assuming that the jump probabilities can be evaluated at the start of the waiting time prior to jumping. For the first time we obtain the linear response characteristic for the first type of the time fractional Fokker?Planck equation systems, and for a comparison we revisit the corresponding result for the second type of the time fractional Fokker?Planck equation systems, and the similarity and difference between them is discussed with an application example. The investigation not only helps in understanding the competition between subdiffusion and time-dependent modulation, but also has significance in accessing the spectral properties of spontaneous fluctuation and the linear dynamic susceptibility of external perturbation in subdiffusive processes.

Observing fluctuating spectral density of subdiffusive overdamped Brownian particles in periodic potentials

The aim of this paper is to develop a simple and efficient method for observing the fluctuating spectral density of subdiffusive Brownian motion in an overdamped periodic potential for exploring the subdiffusive property in frequency domain. Based on the general frame of linear response theory for subdiffusive fractional Fokker–Planck equation systems, an explicit relation between fluctuating spectral density and linear dynamical susceptibility is deduced, and then a method of moments based on the expansion of trigonometric functions is proposed for calculating the linear dynamic susceptibility. With the linear dynamic susceptibility available, the fluctuating spectral density is finally obtained. The numerical results demonstrate that subdiffusion weakens coherent oscillations in the periodic system, but enhances aperiodic components. Our observation embodies the fact of the Mittag–Leffler residence time distribution with an infinite mean in the subdiffusive process from the frequency domain.

Subcritical Hopf Bifurcation and Stochastic Resonance of Electrical Activities in Neuron under Electromagnetic Induction

The FitzHugh–Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity.

Switches in a Genetic Regulatory System under Multiplicative Non-Gaussian Noise.

The non-Gaussian noise is multiplicatively introduced to model the universal fluctuation in the gene regulation of the bacteriophage λ. To investigate the key effect of non-Gaussian noise on the genetic on/off switch dynamics from the viewpoint of quantitative analysis, we employ the high-order perturbation expansion to deduce the stationary probability density of repressor concentration and the mean first passage time from low concentration to high concentration and vice versa. The occupation probability of different concentration states can be estimated from the height and shape of the peaks of the stationary probability density, which could be used to determine the overall expression level. A further concern is the mean first passage time, also referred to as the mean switching time, which can be adopted as an important measure to characterize the adaptability of gene expression to the environmental variation. Through our investigation, it is observed that the non-Gaussian heavy-tailed noise can better induce the switches between distinct genetic expression states and additionally, it accelerates the switching process more evidently compared to the Gaussian noise and the bounded noise.

Effect of spatially correlated noise on stochastic synchronization in globally coupled FitzHugh-Nagumo neuron systems

The phenomenon of stochastic synchronization in globally coupled FitzHugh-Nagumo (FHN) neuron system subjected to spatially correlated Gaussian noise is investigated based on dynamical mean-field approximation (DMA) and direct simulation (DS). Results from DMA are in good quantitative or qualitative agreement with those from DS for weak noise intensity and larger system size. Whether the consisting single FHN neuron is staying at the resting state, subthreshold oscillatory regime, or the spiking state, our investigation shows that the synchronization ratio of the globally coupled system becomes higher as the noise correlation coefficient increases, and thus we conclude that spatial correlation has an active effect on stochastic synchronization, and the neurons can achieve complete synchronization in the sense of statistics when the noise correlation coefficient tends to one. Our investigation also discloses that the noise spatial correlation plays the same beneficial role as the global coupling strength in enhancing stochastic synchronization in the ensemble. The result might be useful in understanding the information coding mechanism in neural systems.

Effect of spatial correlation on stochastic resonance in two linearly interacting noisy bistable oscillators

We investigate the effect of locally correlated spatial noise on the stochastic resonance (SR) phenomenon in two linearly interacting overdamped bistable oscillators using a symmetric series expansion method designed for calculating the long-time probability density function within the linear response range. For positive coupling strength, it is shown that negative correlation has an advantage over both statistical independence and positive correlation for enhancing SR when the bias parameter is small, but for a larger bias parameter or for negative coupling strength, it is found that positive correlation is better than the others. Our observation suggests the complexity in the interaction of correlation and system response, and the result should be useful for weak signal detection and transmission in a correlated noisy background.