Stochastic Bifurcation in the Saccadic System Driven by Noise
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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.Abstract: 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 probability 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.
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Key words:
- saccadic system /
- nystagmus /
- stationary probability density /
- white Gaussian noise
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[1] Robert M P, Michel S, Adjadj E, et al. Benign intermittent upbeat nystagmus in infancy: a new clinical entity[J]. European Journal of Paediatric Neurology, 2015,19(2): 262-265. [2] Moon K H, Lee S A, Ahn J S, et al. Downbeat nystagmus associated with brainstem compression by vertebral artery[J]. Journal of Korean Neurosurgical Society, 2007,41(3): 190-192. [3] Ogawa Y, Itani S, Otsuka K, et al. Intermittent positional downbeat nystagmus of cervical origin[J].Auris Nasus Larynx, 2014,41(2): 234-237. [4] 陈维毅, 杨桂通, 吴文周. 人体眼球的运动模型及相应的动力学方程组[J]. 中国生物医学工程学报, 2000,19(3): 266-271.(CHEN Wei-yi, YANG Gui-tong, WU Wen-zhou. Mechanical model of human eye and corresponding dynamic equations[J]. Chinese Journal of Biomedical Engineering,2000,19 (3): 266-271.(in Chinese)) [5] 陈维毅, 杨桂通, 吴文周. 眼球的运动模型及对钟摆型眼球震颤的模拟分析[J]. 中国生物医学工程学报, 2000,19(2): 185-190, 199.(CHEN Wei-yi, YANG Gui-tong, WU Wen-zhou. Mechanical model of human eye and stimulating analysis of pendular nystagmus[J]. Chinese Journal of Biomedical Engineering,2000,19(2): 185-190, 199.(in Chinese)) [6] Broomhead D S, Clement R A, Muldoon M R, et al. Modelling of congenital nystagmus waveforms produced by saccadic system abnormalities[J]. Biological Cybernetics, 2000,82(5): 391-399. [7] Akman O E, Broomhead D S, Abadi R V, et al. Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system[J]. Journal of Mathematical Biology, 2005,51(6): 661-694. [8] Laptev D, Akman O E, Clement R A. Stability of the saccadic oculomotor system[J]. Biological Cybernetics, 2006,95(3): 281-287. [9] Akman O E, Broomhead D S, Clement R A, et al. Nonlinear time series analysis of jerk congenital nystagmus[J]. Journal of Computational Neuroscience,2006,21(2): 153-170. [10] Barreiro A K, Bronski J C, Anastasio T J. Bifurcation theory explains waveform variability in a congenital eye movement disorder[J]. Journal of Computational Neuroscience,2009,26(2): 321-329. [11] Faisal A A, Selen L P J, Wolpert D M. Noise in the nervous system[J]. Nature Reviews Neuroscience,2000,9(4): 292-303. [12] 顾仁财, 许勇, 郝孟丽, 等. Lévy 稳定噪声激励下的Duffing-van der Pol振子的随机分岔[J]. 物理学报, 2011,60(6): 060513.(GU Cai-yong, XU Yong, HAO Meng-li, et al. Stochastic bifurcations in Duffing-van der Pol oscillator with Lévy stable noise[J]. Acta Physica Sinica,2011,60(6): 060513.(in Chinese))
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