高斯噪声激励下分段线性双稳系统的稳态特性研究

Steady-state characteristics of a piecewise linear bistable potential system driven by Gaussian noises

研究了关联乘性和加性高斯白噪声激励下分段线性双稳系统的稳态特性。通过随机等价变换方法得到了该系统稳态概率密度函数的表达式,讨论了噪声关联性和噪声强度对系统稳态概率密度函数的影响,并通过数值计算发现该系统出现了一些新的随机现象。研究结果表明,乘性噪声强度、加性噪声强度、噪声互关联强度都能使稳态概率密度函数曲线峰的数目发生改变,这说明系统出现了相变现象,且两关联高斯白噪声对系统稳态概率密度具有相同的影响作用。

The steady-state properties of a piecewise linear bistable potential system subjected to correlated multiplicative and additive Gaussian white noises are investigated. Firstly, the expression of the steady state probability distribution function(SPD) is derived by using the stochastically equivalent transformation. Then, effects of cross-correlation strength and noise intensities on SPD are analyzed. After numerical computations, some new nonlinear phenomena are found that the multiplicative noise intensity, the additive noise intensity and the cross-correlation strength can change the number of peaks, which shows that the noise-induced transition phenomenon appears. Meanwhile, influence of the multiplicative Gaussian white noise and the additive Gaussian white noise on SPD is the same.