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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。
Aiming at a kind of simple cortical model proposed by Robinson et al., The bifurcation characteristics of the model under two-way delay are studied. Considering the two-way delay of information transmission between excited neurons and inhibitory neurons, the influence of this condition on the model stability and branch characteristics is discussed and the branch regions are given. Under the condition of white noise introduced into the model, the variation of the cortical potential density with time delay was analyzed. The results show that the delay is an important factor for the dynamic characteristics of the model. The bifurcation region can well reflect the stability of the model. The increase of the delay leads to the decrease of the system stability. The delay phase diagram of the EEG signal shows that the system before and after the seizure Variations and numerical simulations verify the validity of the theory. Studies have shown that the conduction delay between neuronal clusters can change the dynamic characteristics of the model, affecting the stability, the results for the seizures and inhibition of related studies provide a reference.