Houwen Xin

Internal noise stochastic resonance in a circadian clock system

We have studied the influence of internal noise on a circadian clock system using stochastic simulation methods and chemical Langevin equations. It is found that internal noise can induce circadian oscillations, when the corresponding deterministic system does not oscillate. The performance of the noise induced circadian oscillation undergoes a maximum with the variation of the internal noise level, showing the occurrence of internal noise stochastic resonance. Since the magnitude of the internal noise is changed via the variation of the system size, these phenomena also demonstrate a kind of system size resonance.

Stochastic resonance in the absence and presence of external signals for a chemical reaction

A catalytic reduction of NO with CO on Pt(100) surface is adopted to study its response under random perturbation. Noise-induced oscillations and noise-induced frequency shifts have been observed when the system works in the vicinity of the oscillatory region and meanwhile is subjected to random modulation of its feeding speed. Stochastic resonance behavior can be recognized from the noise-induced peak in the power spectrum even though in the absence of external signals. The numerical results have been obtained near supercritical Hopf bifurcation points, but are not confined to the classification of bifurcation. When the system falls into bistable regions, noise can help an external weak signal to induce state-to-state transitions and also shows a stochastic resonance behavior except for the case that the system has an isolated bifurcation scheme.

Effects of colored noise on internal stochastic resonance in a chemical model system

Abstract The phenomenon of internal stochastic resonance (SR) in a chemical model system was studied. The effects of colored noise with finite correlation time were compared with those of white noise without any time correlation. It was shown that the correlation time of noise could affect the peak value of internal SR and the location of the optimal noise intensity for resonance behavior. The application of correlation time in controlling internal SR was discussed.

Internal stochastic resonance in a model system for intracellular calcium oscillations

A model system for intracellular calcium oscillations was investigated when the control parameter was perturbed by noise near a Hopf bifurcation point. Noise-induced oscillations were observed. Furthermore, the output signal-to-noise ratio (SNR) of the system went through a maximum with the increment of noise intensity indicating the occurrence of internal stochastic resonance (SR), which showed the constructive role of noise at the cellular level.

Stochastic resonance in catalytic reduction of NO with CO on Pt(100)

This paper presents a stochastic resonance occurring in a chemical reaction Pt(100)/NO+CO. The results were from numerical simulation of the nonlinear kinetic behavior of a three-variable reaction model obtained from the law of mass actions. The model exhibits a special region in the bifurcation scheme, where a stable node coexists with a stable limit cycle. When one of the control parameters is perturbed by a weak, low frequency periodic signal riding on a suitable external noisy background, transitions between the steady state and oscillatory state may become regular unexpectedly, and signal to noise ratio is thus enhanced at the signal frequency in the Fourier transform power spectrum of the time series output. That refers to stochastic resonance, in which the noise may play a constructive role in the detection of weak signals. The findings may suggest a new method to develop chemical sensitive devices in the field of applications. The paper also discusses the conditions of occurrence of stochastic res...

Effects of internal noise in mesoscopic chemical systems near Hopf bifurcation

The effects of internal noise in mesoscopic chemical oscillation systems have been studied analytically, in the parameter region close to the deterministic Hopf bifurcation. Starting from chemical Langevin equations, stochastic normal form equations are obtained, governing the evolution of the radius and phase of the stochastic oscillation. By stochastic averaging, the normal form equation can be solved analytically. Stationary distributions of the radius and auto-correlation functions of the phase variable are obtained. It is shown that internal noise can induce oscillation; even no deterministic oscillation exists. The radius of the noise-induced oscillation (NIO) becomes larger when the internal noise increases, but the correlation time becomes shorter. The trade-off between the strength and regularity of the NIO leads to a clear maximum in its signal-to-noise ratio when the internal noise changes, demonstrating the occurrence of internal noise coherent resonance. Since the intensity of the internal noise is inversely proportional to the system size, the phenomenon also indicates the existence of an optimal system size. These theoretical results are applied to a circadian clock system and excellent agreement with the numerical results is obtained.

Internal noise-enhanced phase synchronization of coupled chemical chaotic oscillators

The effect of internal noise on phase synchronization of two coupled chemical chaotic oscillators is investigated numerically using chemical Langevin equations. It is found that internal noise can enhance the phase synchronization, and there exists an optimal internal noise level such that the best phase synchronization is achieved. Since the magnitude of the internal noise is changed via the variation of the system size, these phenomena also indicate the existence of an optimal system size.

Stochastic resonance in surface catalytic oxidation of carbon monoxide

Stochastic resonance is a nonlinear cooperative effect between external signal and noise, in which the noise can play a constructive role to increase the signal-to-noise ratio in the detection of a weak signal. A surface catalytic reaction model, to describe oxidization of carbon monoxide carrying out far from equilibrium, was adopted to study the stochastic resonance. By computer simulation, we found noise can induce state-to-state transitions, and stochastic resonance behavior may appear at narrow bistable states or near discontinuous Hopf bifurcations, while a weak periodic signal riding on noise is input controlling.

Noise-induced oscillations and internal stochastic resonance in a model of excitable biomembrane

Abstract The dynamics of the oil–water liquid membrane oscillator driven by external noise was investigated near a Hopf bifurcation point. Noise activated the system producing a sequence of oscillations. The coherence of noise-induced oscillations reached a maximum for a certain noise intensity indicating occurrence of internal stochastic resonance (SR). The constructive role of noise in some sensory cells is discussed.

Stochastic bi-resonance without external signal in the CO+O2 catalytic oxidation reaction system

The noisy dynamic behavior of a surface catalytic reaction model to describe the oxidation of carbon monoxide is investigated when the control parameter is perturbed by external noise near a supercritical Hopf bifurcation point. Noise induced coherent oscillation (NICO) is observed and the NICO strength goes through two maxima with the increment of the noise intensity D from zero, characteristic of the occurrence of stochastic multiresonance without external signal. The frequency of the NICO also increases with the increment of D.