ZHANG Xiang-yun, WU Zhi-qiang. Stochastic Bifurcation in the Saccadic System Driven by Noise[J]. Applied Mathematics and Mechanics, 2017, 38(1): 126-132. doi: 10.21656/1000-0887.370513
Citation: ZHANG Xiang-yun, WU Zhi-qiang. Stochastic Bifurcation in the Saccadic System Driven by Noise[J]. Applied Mathematics and Mechanics, 2017, 38(1): 126-132. doi: 10.21656/1000-0887.370513

Stochastic Bifurcation in the Saccadic System Driven by Noise

doi: 10.21656/1000-0887.370513
Funds:  The National Natural Science Foundation of China(11372211; 11672349)
  • Received Date: 2016-09-11
  • Rev Recd Date: 2016-12-28
  • Publish Date: 2017-01-15
  • 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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