运用Liouville 方程和诺维科夫原理,解出了关联噪声和周期信号共同驱动的 非对称双稳系统的近似福克-普朗克方程,并求解了其稳态概率密度函数。在此基础上,分析了乘性噪声强度D、加性噪声强度Q、 噪声间关联系数λ, 周期信号振幅A、频率Ω以及系统非对称参数r 等对稳态概率密度分布曲线的影响。结果表明: 1)噪声强度及其关联、周期信号振幅、 系统非对称参数的改变均能引起稳态概率密度分布曲线单峰结构和双峰结构之间的转换, 即能够诱导非平衡相变产生; 2)周期信号频率改变时,没有非平衡相变发生; 3)当系统非对称参数为零时,稳态概率密度分布 曲线具有关于x=0的对称结构;当系统非对称参数不等于零时,其对称结构被破坏。

By virtue of the Liouville equation and Novikov theorem, the approximate Fokker-Planck equation was derived, and the analytic expression of the stationary probability distribution (SPD) was obtained in an asymmetric bistable system driven by cross-correlated multiplicative white noise and additive white noise with periodic signal. Based on the computed results, effects of the following parameters, including intensity of noises and their correlation, the amplitude and frequency of the periodic signal, and the asymmetric parameter of system on the SPD were investigated. Numerical results show that: 1) The intensity of noises and their correlation, amplitude of periodic signal, and asymmetric parameter of the system can induce the SPD transition from bimodal to unimodal in structure, i.e., a non-equilibrium phase transition is generated. 2) There is no non-equilibrium phase transition as frequency of the periodic signal varies. 3) The structure of the SPD exhibits a symmetrical structure at x=0 in the case of r=0, while the symmetry of SPD at x=0 is destroyed if the asymmetric parameter of the system r≠0.