一类具有双向时延的脑皮层电模型的分支研究

系统仿真学报 ›› 2015, Vol. 27 ›› Issue (12): 3063-3069.

一类具有双向时延的脑皮层电模型的分支研究

李春胜¹, 张雪²

1.沈阳工业大学电气工程学院, 辽宁沈阳 110870;
2.东北大学理学院, 辽宁沈阳 110819

收稿日期:2014-07-17 修回日期:2015-05-22 出版日期:2015-12-08 发布日期:2020-07-30
作者简介:李春胜(1978),男,江苏连云港,博士,讲师,研究方向为癫痫脑电信号的分析处理、神经系统的建模与仿真。
基金资助:
辽宁省教育厅科技项目(201134121); 中央高校基本科研业务费(N140504005)

Research on Bifurcation of a Class of Cortical EEG Model with Time Delay

Li Chunsheng¹, Zhang Xue²

1. School of Electrical Engineering, Shenyang University of Technology, Shenyang 110870, China;
2. School of Sciences, Northeastern University, Shenyang 110819, China

Received:2014-07-17 Revised:2015-05-22 Online:2015-12-08 Published:2020-07-30

摘要/Abstract

摘要： 针对Robinson等人提出的一类简约脑皮层电模型,研究双向时延条件下模型的分支特性。考虑到兴奋型神经元和抑制型神经元之间信息传递的双向时延,讨论了该条件对模型稳定性和分支特性的影响,并给出了分支区域。在模型引入白噪声条件下,分析了皮层电位谱密度随时延的变化关系。结果说明,时延是模型动态特征变化的重要因素,分支区域能很好的反映模型稳定性,时延增加导致了系统稳定性下降,脑电信号的延时相图说明了癫痫发作前后的系统变化,数值仿真验证了理论的有效性。研究表明神经元集群间传导时延可改变模型的动态特性,影响稳定性,其结果可为癫痫发作与抑制等相关研究提供借鉴。

关键词: EEG模型, 传导时延, Hopf分支, 稳定性, 癫痫

Abstract: The bifurcation characters of a cortical-model with bidirectional time delays were studied, proposed by Robinson, et al. before. Considering transmitting delay between excitatory and inhibitory populations, the stability, bifurcation characters and bifurcation region were achieved. The relationship of cortical potential spectrum density and transmit delay was analyzed when white noise was introduced. Result shows that time delay between different population acts as an important role of model’s dynamic characters and stability, and numerical simulation verifies the theoretical analysis. This research shows the importance of transmit delay in cortical-model, and provides theoretical illustration for further research of epileptic seizure.

Key words: EEG model, time delay, Hopf bifurcation, stability, epilepsy

中图分类号:

TP.391.9

李春胜, 张雪. 一类具有双向时延的脑皮层电模型的分支研究[J]. 系统仿真学报, 2015, 27(12): 3063-3069.

Li Chunsheng, Zhang Xue. Research on Bifurcation of a Class of Cortical EEG Model with Time Delay[J]. Journal of System Simulation, 2015, 27(12): 3063-3069.

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