中文摘要：

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 （FitzHugh-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。

英文摘要：

Recently, the dynamics problems of nonlinear systems driven by noises have attracted considerable attention. The researches indicate that the noise plays a determinative role in system evolution. This irregular random interference does not always play a negative role in the macro order. Sometimes it can play a positive role. The various effects of noise are found in physics, biology, chemistry and other fields, such as noise-induced non-equilibrium phase transition, noise-enhanced system stability, stochastic resonance, etc. Especially, in the field of biology, the effects of noise on life process are significant. At present, a large number of researchers have studied the kinetic properties of the neuron system subjected to noises. However, these studies focus on the Gaussian noise, while the researches about non-Gaussian noise are less. In fact, it is found that all the noise sources among neuronal systems, physical systems and biological systems tend to non-Gaussian distribution. So it is reasonable to consider the effects of the non-Gaussian noise on systems, and it is closer to the actual process. Therefore, it has some practical significance to study the FHN system driven by the non-Gaussian noise and analyze the kinetic properties of this system. In this work, we study the stationary probability distribution （SPD） in FitzHugh-Nagumo （FHN） neural system driven by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Using the path integral approach and the unified colored approximation, the analytical expression of the stationary probability distribution is first derived, and then the change regulations of the SPD with the strength and relevance between multiplicative noise and additive noise are analyzed. After that, the simulation results show that the intensity of multiplicative noise, the intensity of additive noise, the correlation time of the non-Gaussian noise and the cross-correlation strength between noises can induce non-equilibrium phase transition. This means tha