双色噪声激励下FHN神经元系统的稳态性质

应用统一色噪声理论研究了双色噪声激励下一维FitzHugh-Nagumo (FHN)神经元系统的动力学性质,即稳态概率分布函数和其平均值. 给出了FHN神经元系统的稳态概率密度和平均值的解析表达式. 结果表明: 乘性噪声的自关联时间τ ₁、加性噪声的自关联时间τ ₂、加性噪声强度α 和乘性噪声强度D都能够诱导非平衡相变的产生. α和D的增大有利于系统从激发态向静息态转换. τ₁, τ₂的增大有利于系统从静息态向激发态转换. 噪声强度和其自关联时间的作用完全相反.     

加性噪声对激光一级相变类比的影响

从单模激光场的增益－噪声模型出发,导出了激光场定态强度分布函数,研究了定态分布函数的极值点随加性噪声、乘性噪声和注入信号的变化情况。结果表明,乘性噪声是使激光系统出现一级相变类比的关键因素,注入信号使相变行为减弱,而加性噪声却使得定态分布中极值点的数量和位置出现来回跳跃式变化。     

噪声对集合种群稳定性的影响

本文在Levins模型的基础上研究了噪声对集合种群的稳定性的影响. 应用Fokker-Planck方程得到了系统的稳态概率分布函数和平均灭绝时间. 经过数值分析,结果如下: 无关联(λ=0 λ为加性噪声和乘性噪声之间的关联强度)时, 加性噪声强度α和乘性噪声强度D均弱化集合种群的稳定性; 噪声之间关联(λ≠0)时, 随着λ的增大,系统的稳定性被增强. 当-(c-e-D)²/(4c√Dα)<λ<1时, λ诱导"共振抑制"现象. D存在一个临界值, 小于临界值时, D可以增强系统的稳定性.     

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN(Fitz Hugh-Nagumo)神经元系统.利用路径积分法和统一色噪声近似,推导出该系统的定态概率密度函数表达式.通过研究发现,乘性噪声强度D、加性噪声强度Q、噪声自关联时间τ以及互关联系数λ均可以诱导系统产生非平衡相变现象,而非高斯参数q却不可以诱导系统产生非平衡相变现象.此外,我们还发现参数D和λ的增大有利于神经元系统从激发态向静息态转换,Q和τ的增大有利于神经元系统从静息态向激发态转换,q的增大会使得神经元系统停留在静息态的概率增加.     

非高斯噪声激励下FHN神经元系统的定态概率密度与平均首次穿越时间

研究了非高斯噪声激励下的FHN神经元系统,应用路径积分法和统一色噪声近似得到系统的定态概率密度函数和平均首次穿越时间表达式.发现了加性噪声强度Q能够诱导非平衡相变的产生,乘性噪声强度D、偏离参数p及关联时间τ₀均不能诱导非平衡相变发生;非高斯噪声的存在缩短了细胞神经元系统静息态和激发态之间的转化时间,有利于神经元信息的传递. 关键词： FHN神经元系统 非高斯噪声 定态概率密度 平均首次穿越时间     

色关联的色噪声驱动的分段非线性模型的平均首次穿越时间

研究了色关联的乘性高斯色噪声和加性高斯色噪声驱动的分段非线性系统中, 噪声强度和相关时间对平均首次穿越时间的影响. 利用一致有色噪声近似方法和最速下降方法, 推导出系统平均首次穿越时间的表达式. 研究结果表明: 系统的平均首次穿越时间随着乘性噪声的增加会出现单峰结构, 即“共振”现象, 峰值会随着加性噪声强度和噪声之间关联强度的增加而减小. 而平均首次穿越时间作为加性噪声的函数呈单调曲线, 说明乘性噪声和加性噪声对平均首次穿越时间的影响不同. 此外, 乘性和加性噪声关联时间以及互关联时间在正关联时和负关联时 对系统平均首次穿越时间的影响是不同的. 关键词： 色噪声 分段非线性系统 平均首次穿越时间     

Colored Noise in First-order-like Phase Transition of a Laser System

The decoupling theory is employed to analyze the multiplicative colored noise in a single mode laser system. Steady state intensity distribution function is derived when colored noise is included in the laser system. The first-order-like phase transition driven by multiplicative colored noise is investigated and compared with the case of multiplicative white noise. It is shown that the noise correlation time can affect the parameter plane of the first-order-like phase transition. The steady state intensity distributions in a laser system is changed greatly with noise correlation time τ.     

Colored Noise in First-order-like Phase Transition of a Laser System

The decoupling theory is employed to analyze the multiplicative colored noise in a single mode laser system. Steady state intensity distribution function is derived when colored noise is included in the laser system. The first-order-like phase transition driven by multiplicative colored noise is investigated and compared with the case of multiplicative white noise. It is shown that the noise correlation time can affect the parameter plane of the first-order-like phase transition. The steady state intensity distributions in a laser system is changed greatly with noise correlation time τ.     

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance.     

乘性噪音和加性噪音效应对脉孢菌生物钟体系内信号随机共振的增强

利用有和无外信号作用的脉孢菌生物钟体系,研究了与加性噪音相关或不相关的乘性噪音对加性噪音诱导出的内信号随机共振的影响作用.结果表明：无外信号的情况下,不论加性和乘性噪音相关与否,当乘性噪音强度小于临界值时,乘性噪音的加入使加性噪音诱导产生的内随机共振强度得到增强;当大于其临界值时,加性噪音的随机共振强度却得不到进一步增强,这说明脉孢菌生物钟体系能抵抗外噪音的干扰而维持自身的生理节奏.当加入外信号时,对于乘性和加性噪音不相关的情况,发现存在最佳频率（0.003 Hz）的外信号能使加性噪音诱导出的内信号随机共 关键词： 噪音 脉孢菌生物钟体系 内信号随机共振     

Steady-state analysis subject to a coloured and a white additive of a bistable system multiplicative noise noise with coloured cross-correlated noises

The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times T1 and T2. After introducing a dimensionless parameter R（R = α/D, D is the intensity of the multiplicative noise and a is the intensity of the additive noise）, and performing the numerical computations, we find the following points： （1） For the case of R 〉 1, A （the intensity of correlation between additive and multiplicative noises）, T1 and T2 can induce the stationary probability distribution （SPD） transition from bimodal to unimodal in structure, but for the cases of R _〈 1, the bimodal structure is preserved; （2） a can also induce the SPD transition from bimodal to unimodal in structure; （3） the bimodal structure of the SPD exhibits a symmetrical structure as D increases.     

Effect of time delay in FitzHugh-Nagumo neural model with correlations between multiplicative and additive noises

We study the effect of time delay in the FitzHugh-Nagumo neural model with correlations between multiplicative and additive noise terms. Based on the corresponding Fokker-Planck equation, the explicit expressions of the stationary probability distribution function (SPDF), the mean first passage time (MFPT) and the signal-to-noise ratio (SNR) are obtained, respectively. Research results show that: (i) the system undergoes a succession of two phase transitions (i.e., the reentrance phenomenon) as the noise correlation parameter is increased and a (single) phase transition as the time delay is increased. (ii) The MFPT as a function of the multiplicative noise intensity exhibits a maximum. This maximum for MFPT identifies the noise enhanced stability (NES) effect, the noise correlation parameter intensifies the NES effect while the time delay, and the additive noise intensity weakens it. (iii) The existence of a maximum in the SNR as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance (SR) phenomenon, the noise correlation parameter enhances the SR while the time delay, and the additive noise intensity weaken it.     

Multiplicative non-Gaussian noise and additive Gaussian white noise induced transition in a piecewise nonlinear model

We study the transition problems in a piecewise nonlinear model induced by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Firstly, applying the path integral approach, the unified colored noise approximation, the analytical expression of the steady-state probability density function (SPD) is derived. Then the change regulation of the SPD is analyzed with the change of the strength and relevance of multiplicative noise and additive noise. From numerical computations we obtain some new nonlinear phenomena: the transition can be induced by the cross-correlation strength between noises, the non-Gaussian noise intensity and the Gaussian noise intensity as well as the non-Gaussian noise deviation parameter. This indicates that the effect of the non-Gaussian noise intensity on SPD is the same as that of the Gaussian noise intensity. Moreover, we also find the correlation time of the non-Gaussian noise can not induce the transition.     

Stochastic resonance in a bias linear system with multiplicative and additive noise

In this paper, the stochastic resonance in a bias linear system subjected multiplicative and additive dichotomous noise is investigated. Using the linear-response theory and the properties of the dichotomous noise, this paper finds the exact expressions for the first two moments and the signal-to-noise ratio (SNR). It is shown that the SNR is a non-monotonic function of the correlation time of the multiplicative and additive noise, and it varies non-monotonously with the intensity and asymmetry of the multiplicative noise as well as the external field frequency. Moreover, the SNR depends on the system bias, the intensity of the cross noise between the multiplicative and additive noise, and the strength and asymmetry of the additive noise.     

Colored Gaussian noises induced stochastic resonance and stability transition for an insect growth system driven by a multiplicative periodic signal

In this paper, we focus on investigating the steady-state shift behaviors and the stochastic resonance phenomenon (SR) for a biological insect population system with a multiplicative periodic signal caused by the terms of the colored multiplicative and additive noises. Our research results imply that the multiplicative noise and the self-correlation of the additive noise can weaken the stability of the biological system and restrain the growth of the insect population, while the additive noise and the self-correlation time of the multiplicative noise can strengthen the stability of the insect system and facilitate the biological population to breed. As regards to the phenomenon of the SR evoked by a multiplicative periodic signal, noise terms and their correlation times, the computed results show that the additive noise intensity M and the self- correlation time τ₁ of the multiplicative noise can both improve the SR effect. Inversely, the multiplicative noise intensity Q and the self-correlation time τ₂ of the additive noise can suppress together the SR phenomenon. Whereas, it should be pointed out that in the SNR-Q and SNR-M plots, the two self-correlation times can both motivate a resonant peak, but not change the peak value of the SNR no matter how the two noise correlation times vary.     

Resonant-Like Activation in a Bistable System with Noise and Time Delay

A bistable system with noise and time delay is investigated. Theoretical analysis and stochastic simulation show that： （i） In the ease of a system driven only by multiplicative Gaussian white noise, the mean first-passage time for a particle to reach the other stable state from one stable state exhibits a minimum with respect to delay time, i.e., a resonant-like activation （RA） phenomenon. （ii） In the action of additive and multiplicative noise, as the additive noise intensity increases, no matter whether a correlation between the two types of noise exists or not, the RA gradually disappears. （iii） The correlation strength between the two types of noise does not influence the existence of the RA.     

Logistic系统跃迁率的时间延迟效应

本文研究了时间延迟对Logistic系统从亚稳态跃迁到稳定态的跃迁率的影响. 假设在细胞演化过程中细胞衰减存在时间延迟,利用小延迟时间条件下一阶近似方法和最陡下降法导出了系统的跃迁率解析式. 数值计算结果表明,内噪声,外噪声和内外噪声之间的关联促使系统从亚稳态跃迁到稳定态, 而时间延迟阻碍了系统从亚稳态到稳定态的跃迁, 即时间延迟增强了系统亚稳态的稳定性. 关键词： Logistic模型 跃迁率 时间延迟 噪声     

关联白噪声驱动的具有时间延迟的Logistic系统

关联白噪声驱动的具有时间延迟的Logistic系统可更真实的反映肿瘤细胞的增长问题,本文通过小时间延迟近似方法对由关联白噪声驱动的具有时间延迟的Logistic系统进行了研究,得到了系统的稳态概率密度,并进一步分析了加性和乘性噪声强度,噪声关联时间和时间延迟对稳态概率密度的影响以及噪声诱导的非平衡相变现象. 关键词： Logistic系统 关联白噪声 时间延迟 非平衡相变     

Combined action of time-delay and colored cross-associated multiplicative and additive noises on stability and stochastic resonance for a stochastic metapopulation system

In this paper, the transition between the stable state of a big density and theextinction state and stochastic resonance (SR) for a time-delayed metapopulation systemdisturbed by colored cross-correlated noises are investigated. By applying the fastdescent method, the small time-delay approximation and McNamara and Wiesenfeld’s SRtheory, we investigate the impacts of time-delay, the multiplicative, additive noises andcolored cross-correlated noise on the SNR and the shift between the two states of thesystem. Numerical results show that the multiplicative, additive noises and time-delay canall speed up the transition from the stable state to the extinction state, while thecorrelation noise and its correlation time can slow down the extinction process of thepopulation system. With respect to SNR, the multiplicative noise always weakens the SReffect, while noise correlation time plays a dual role in motivating the SR phenomenon.Meanwhile, time-delay mainly plays a negative role in stimulating the SR phenomenon.Conversely, it could motivate the SR effect to increase the strength of thecross-correlation noise in the SNR-β plot, while the increase of additive noiseintensity will firstly excite SR, and then suppress the SR effect.     

Parameter-induced stochastic resonance in an over-damped linear system

Stochastic resonance (SR) in an over-damped linear system subjected to an excitation of bias signal modulated noise with multiplicative and additive noises is investigated. We obtain the exact expressions of the first two moments and the signal-to-noise ratio (SNR) of the output by using linear-response theory. The SNR depends non-monotonically on the intensity and the correlation time of multiplicative noise, the correlation time of additive noise, the intensity of the cross noise between multiplicative and additive noise, as well as the external field frequency. The conventional SR, the SR in a broad sense and the bona fide SR are found in the system. The influences of the asymmetries of multiplicative and additive noise, the correlation rate of the cross noise, the intensity of additive noise, the amplitude of signal and the bias on the SNR are analyzed. Moreover, we pointed out that SR can be realized by tuning the system parameter with fixed noise, i.e., parameter-induced stochastic resonance (PSR) exists.