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在过去的几十年里,噪声的积极作用被广泛研究.以往研究中,人们通常认为噪声遵循高斯分布.然而,有关的生物学实验研究表明,在诸如神经元等感官体系中存在非高斯噪声.近十年,一类特殊形式的非高斯噪声在非线性动力学体系(包括生物体系和化学体系)中的作用受到人们的关注.本文中,我们用数值模拟方法研究该类非高斯噪声对NO+CO/Pt(100)催化还原体系反应速率振荡的影响.反应基本步骤如下:反应动力学方程为其中θCO,θNO和θO分别代表CO,NO和O的覆盖度;ki(i=1,2,…,6)是速率常数,假定CO和NO的吸附速率常数相等,即k1=k3.分岔分析表明,在7PCO=3×10-mbar条件下,当PNhO=3.044×10-7mbar时方程(2)出现Hopf分岔.吸附能EadCO,NO满足关系CO,NOCO,NO2Ead(θ)=Ead(0)-k7θ,θ是CO和NO覆盖度之和θ=θNO+θCO.由NO偏压PNO涨落引进噪声ξ(t):PNO=PN0O[1+ξ(t)],这里PN0O=3.043×10-7mbar是未经噪声调制的NO偏压,处于Hopf分岔点外并靠近分岔点.设ξ(t)具有非高斯分布形式:高斯白噪声,满足ε(t)=0,ε(t)ε(t′)=2Dδ(t-t′),D和τ分别与噪声强度和关联时间有关.q代表ξ(t)与高斯噪声的偏离.采用显式Euler法对方程(2)～(4)进行数值计算,步长取0.001s.用功率谱和信噪比对速率振荡状态进行定量描述.首先研究了噪声强度对速率振荡的影响,发现在一定τ和q条件下,存在适当的D值,使速率振荡周期性最强,证明出现了噪声强度诱导随机共振现象.然后,重点研究了偏离度q的影响,发现随着q的增加,功率谱峰出现多次升高、变窄和下降、变宽的现象,相应地,信噪比曲线上出现多个峰值.这些变化充分证明了“偏离度诱导多次共振”现象的产生.由于非高斯色噪声与高斯噪声的偏离决定了噪声几率分布,而不同几率分布代表不同的噪声类型,因此,“偏离诱导多次共振”现象不仅表明非高斯噪声与高斯噪声的偏离可以多次加强该体系速率振荡,而且更重要的是,它意味着,除高斯噪声外,其他类型噪声也可以加强表面催化体系反应速率振荡.
In the past few decades, the positive role of noise has been extensively studied.In the past, it was generally considered that noise follows the Gaussian distribution.However, relevant biological experimental studies have shown that there exists non-Gaussian noise in sensory systems such as neurons In recent ten years, the role of a special kind of non-Gaussian noise in nonlinear dynamical systems (including biological systems and chemical systems) has received much attention. In this paper, we study the non-Gaussian noise pairs NO + CO / Pt (100) catalytic reduction system reaction rate oscillation.The basic reaction steps are as follows: The reaction kinetics equation is where θCO, θNO and θO represent the coverage of CO, NO and O, respectively; 2, ..., 6) is the rate constant, assuming that the adsorption rate constants of CO and NO are equal, ie k1 = k3. Bifurcation analysis shows that when PNhO = 3.044 × 10-7mbar at 7PCO = 3 × 10-mbar Hopf bifurcation appears in Eq. (2). The adsorption energies EadCO and NO satisfy the relations CO, NOCO, NO2Ead (θ) = Ead (0) -k7θ, θ is the sum of CO and NO coverage θ = θNO + θCO. PNO = PN0O [1 + ξ (t)], where PN0O = 3.043 × 10-7mbar is the noise-free NO bias at Hopf Ξ (t) has a non-Gaussian distribution: Gaussian white noise satisfying ε (t) = 0, ε (t) ε (t ’) = 2Dδ (tt’), D And τ are related to the noise intensity and the correlation time, respectively, q represents the deviation of ξ (t) from the Gaussian noise, and the equations (2) ~ (4) And signal-to-noise ratio (SNR) are described quantitatively.Firstly, the effect of noise intensity on velocity oscillation is studied and it is found that there is an appropriate value of D for a certain τ and q conditions, which results in the strongest periodicity of velocity oscillation, which proves that noise Then the phenomenon of stochastic resonance is induced by the intensity.Furthermore, the influence of the deviation degree q is studied emphatically, and it is found that with the increase of q, the power spectrum peaks appear multiple times, narrowing, falling and widening. Correspondingly, These variations show that the deviation of degree of deviation induces multiple resonance phenomenon.Due to the deviation of non-Gaussian noise from Gaussian noise, the distribution of noise probability is determined, and the different probability distributions represent different types of noise , Therefore, the phenomenon of “deviation inducing multiple resonance” not only shows that the non-Gaussian noise and Gaussian noise are biased More importantly, it means that the system’s rate oscillations can be enhanced more than once, and more importantly, it means that in addition to Gaussian noise, other types of noise can also enhance the surface catalytic system reaction rate oscillations.