Effects of time delay on stochastic resonance of a periodically driven linear system with multiplicative and periodically modulated additive white noises

Stochastic resonance （SR） of a periodically driven time-delayed linear system with multiplicative white noise and periodically modulated additive white noise is investigated. In the condition of small delay time, an approximate analytical expression of output signal-to-noise ratio （SNR） is obtained. The analytical results indicate that （1） there exists a resonance peak in the curve for SNR versus time delay; （2） the time delay will suspend the SR dramatically for SNR versus other parameters of the system, such as noise intensity, correlation intensity, and signal frequency, once a certain value is reached, the SR phenomenon disappears.

Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

This paper investigates the stochastic resonance （SR） phenomenon induced by the multiplicative periodic signal in a cancer growth system with the cross-correlated noises and time delay. To describe the periodic change of the birth rate due to the periodic treatment, a multiplicative periodic signal is added to the system. Under the condition of small delay time, the analytical expression of the signal-to-noise ratio RSNR is derived in the adiabatic limit. By numerical calculation, the effects of the cross-correlation strength λ and the delay time τ on RSNR are respectively discussed. The existence of a peak in the curves of RSNR as a function of the noise intensities indicates the occurrence of the SR phenomenon. It is found that λ and τ play opposite role on the SR phenomenon, i.e., the SR is suppressed by increasing λ whereas it is enhanced with the increase of τ, which is different from the case where the periodic signal is additive.

Stochastic Resonance of a Periodically Driven Bistable System with Two Different Kinds of Time Delays

In this paper, we study the phenomenon of stochastic resonance （SR） in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there, are two different kinds of time delays existed in the deterministic and fluctuating forces, respectively. Using the small time delay approximation and the theory of signal-to-noise ratio （SNR） in the adiabatic limit, the expression of SNR is obtained. The effects of the delay time T in the deterministic force, and the delay time 8 in the fluctuating force on SNR are discussed. Based on the numerical computation, it is found that： （i） There appears a reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR when the value of the time delay θ is increased. （ii） SR can be realized by tuning the time delay T or 8 with fixed noise, i.e., delay-induced stochastic resonance （DSR） exists.

Time Delay Induced Stochastic Resonance in One Species Competition Ecosystem without a Periodic Signal

One-species competition ecosystem with noise and time delay was investigated as not driven by a periodic force.The results show that the time delay is responsible for stochastic resonance of the system as delay time is smaller than critical point of the Hopf bifurcation.

Robust stabilization of stochastic differential inclusion systems with time delay

This paper is concerned with robust stabilization of stochastic differential inclusion systems with time delay. A nonlinear feedback law is established by using convex hull quadratic Lyapunov function such that the closed-loop system is exponentially stable in mean square. Sufficient conditions for the existence of the feedback are obtained via linear matrix inequalities （LMIs）. An example is given to illustrate the effectiveness of the proposed method.

On passivity of state delayed stochastic jump systems

Based on the definition of passivity extended from deterministic system, the sufficient condition on passivity of stochastic jump system is given against unknown state time delay. By means of memoryless state feedback, a class of state delayed stochastic jump systems may be led to passive. The feedback controllers are mode-dependent and can be constructed in terms of the solutions of a set of coupled linear matrix inequalities. A numerical example illustrates the results.

Further Results on Delay-distribution-dependent Robust Stability Criteria for Delayed Systems

This paper concerns the robust stability analysis of uncertain systems with time delays as random variables drawn from some probability distribution. The delay-distribution-dependent criteria for the exponential stability of the original system in mean square sense are achieved by Lyapunov functional method and the linear matrix inequality （LMI） technique. The proposed approach involves neither free weighting matrices nor any model transformation, and it shows that the new criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Noise transmission and delay-induced stochastic oscillations in biochemical network motifs

With the aid of stochastic delayed-feedback differential equations, we derive an analytic expression for the power spectra of reacting molecules included in a generic biological network motif that is incorporated with a feedback mechanism and time delays in gene regulation. We systematically analyse the effects of time delays, the feedback mechanism, and biological stochasticity on the power spectra. It has been clarified that the time delays together with the feedback mechanism can induce stochastic oscillations at the molecular level and invalidate the noise addition rule for a modular description of the noise propagator. Delay-induced stochastic resonance can be expected, which is related to the stability loss of the reaction systems and Hopf bifurcation occurring for solutions of the corresponding deterministic reaction equations. Through the analysis of the power spectrum, a new approach is proposed to estimate the oscillation period.

Delay-Dependent Exponential Stability of Stochastic Delayed Recurrent Neural Networks with Markovian Switching

The exponential stability problem is investigated for a class of stochastic recurrent neural networks with time delay and Markovian switching. By using Ito＇s differential formula and the Lyapunov stability theory, sufficient condition for the solvability of this problem is derived in term of linear matrix inequalities, which can be easily checked by resorting to available software packages. A numerical example and the simulation are exploited to demonstrate the effectiveness of the proposed results.

Stability Analysis for Stochastic Delayed High-order Neural Networks

In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibtium paint in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities （LMIs）. Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.

含信号调制噪声和频率波动的时滞分数阶振子的随机共振

本文研究了含信号调制噪声和频率波动的小时滞线性分数阶振子的随机共振.利用分数阶Shapiro-Loginov公式和Laplace变换技巧,本文首先推导了系统响应的一阶稳态矩和稳态响应振幅增益(Output Amplitude Gain, OAG)的解析表达式,然后讨论了分数阶、时滞和噪声参数对OAG的影响.结果显示:各参数对OAG的影响均呈现非单调变化的特点,表明系统出现广义随机共振.特别地,分数阶与时滞的协同作用可能诱导随机共振的多样化.这就为在一定范围内调控随机共振提供了可能.

具有随机特征频率和延迟核函数的分数阶线性振荡器中的随机共振

研究了具有延迟核函数和随机特征频率的分数阶线性振荡器中的随机共振(stochastic resonance,SR)现象。基于线性系统理论,利用拉普拉斯变换,推导出了分数维振荡器系统输出幅度(system output amplitude,SOA)的解析表达式。分析表明,SOA是核函数延迟时间的周期函数。在SOA与噪声相关率、噪声幅值、分数维数的关系曲线上都发现了随机共振现象。分析了SOA与系统参数及噪声稳态概率间的非单调依赖行为。

A Guaranteed Cost Approach to Dynamic Output Feedback Control for Neutral-Type Markovian Jumping Stochastic Systems

This paper is devoted to investigating the dynamic output feedback(DOF)control problem of Markovian jump neutral-type stochastic systems with a guaranteed cost function.Both of the state and measurement equations contain time delays.Mode-dependent DOF controllers are first designed such that the closed-loop system is asymptotically stable in mean-square and an adequate performance level of this system is guaranteed.Then,sufficient conditions for the solvability of this problem are derived in the form of linear matrix inequalities(LMIs).A numerical example is presented to reveal the effectiveness of our findings.

噪声交叉关联程度受时间周期调制下单模激光的光强关联时间

用线性化近似方法计算了噪声间关联程度λ受时间周期调制下单模激光系统的光强关联时间T,结果表明,无论λ=0,λ>0或λ<0,T随量子噪声强度D和抽运噪声强度Q的变化均呈单调增长且最终趋于饱和(T=1),只是当λ<0时T随Q的变化曲线出现一极小值(存在抑制现象);当λ=0时,T不随时间周期调制频率Ωλ变化,当λ>0和λ<0,Ωλ取值小时T-Ωλ曲线出现高频振荡,随着Ωλ值增大振荡频率变低,振幅变小,最后趋于与λ=0的T值一致。