| 一类时延脑电模型的分岔研究及其控制 |
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| 引用本文： | 李春胜,王宏,张雪.一类时延脑电模型的分岔研究及其控制[J].东北大学学报(自然科学版),2010,31(6):773-776. |
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| 作者姓名： | 李春胜 王宏 张雪 |
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| 作者单位： | 东北大学中荷生物医学与信息工程学院,辽宁,沈阳,110004;东北大学机械工程学院,辽宁,沈阳,110004;东北大学理学院,辽宁,沈阳,110004 |
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| 基金项目： | 国家自然科学基金，中央高校基本科研业务费资助项目 |
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| 摘 要： | 基于Robinson等人对一类简约脑皮层电模型的研究,对该模型的分叉特性进行了研究.考虑到兴奋型神经元和抑制型神经元之间信息传递的延时,讨论了延时对简约模型稳定性的影响,并给出了模型发生Hopf分岔的条件.结果表明,当时延在一定的阈值内,模型可以保持其稳定状态.进一步地,针对该模型设计了导数反馈控制器,消除了Hopf分岔现象.数值仿真验证了理论的有效性.
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| 关 键 词： | 脑电模型 时延 稳定性 Hopf分岔 导数反馈控制 |
Bifurcation of a Class of Time-Delayed EEG Models and Its Control |
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| LI Chun-sheng,WANG Hong,ZHANG Xue.Bifurcation of a Class of Time-Delayed EEG Models and Its Control[J].Journal of Northeastern University(Natural Science),2010,31(6):773-776. |
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| Authors: | LI Chun-sheng WANG Hong ZHANG Xue |
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| Institution: | (1) School of Sino-Dutch Biomedical and Information Engineering, Northeastern University, Shenyang 110004, China; (2) School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China; (3) School of Sciences, Northeastern University, Shenyang 110004, China |
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| Abstract: | Robinson et al studied a class of reduced EEG model, which was discussed with aim to understand its bifurcation character. Considering the time delay of information transmission between the excitatory and inhibitory neuronal population, the effect of time delay on the stability of the reduced model was studied, as well as the conditions under which the Hopf bifurcation occurs. The results showed that the reduced model can keep up its stability when time delay is restricted within a certain threshold. Furthermore, a derivative feedback controller was designed to eliminate the Hopf bifurcation. Numerical simulation verified theoretically the effectiveness of the conclusions as above. |
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