中文摘要：

研究了眼动系统在神经噪声作用下的随机分岔现象.首先,基于水平眼动系统模型,用加性的Gauss（高斯）白噪声模拟神经系统中的噪声,建立眼动系统的随机动力学模型.其次,利用数值算法得到眼球运动位移的Poincaré分岔图和系统在不同参数下的位移和速度的稳态联合概率密度以及位移的稳态概率密度.研究发现：噪声强度和抑制性神经元的作用强度都能诱导产生随机P分岔现象,使得位移的稳态概率密度出现峰的个数从1到3的转换,间歇性眼球震颤产生.此外,还发现当抑制性神经元的作用强度增大到一定值时,稳态概率密度始终呈现单峰结构.该结论对此类疾病的治疗有一定的指导作用.

英文摘要：

The stochastic bifurcation in the saccadic system driven by noise was investigated. Firstly, the stochastic dynamic model was established by adding the additive white Gaussian noise into the existing bilateral model for the horizontal saccadic system. Secondly, the stationary joint probability density of the system displacement and velocity and the stationary probabil- ity density of the displacement with different parameters were obtained with the numerical method. Then, the results show that noise intensity and inhibitory strength of omnipause neurons may induce the stochastic P bifurcation and the number of peaks on the stationary probability density curve of displacement changes from 1 to 3 and intermittent nystagmus occurs. It is also shown that when the inhibitory strength of omnipause neurons is large enough, the stationary probability density is always unimodal and the intermittent nystagmus disappears, which has some significance for the disease treatment.