Zheng Qianqian, Shen Jianwei, Zhang Rui, Guan Linan, Xu Yong
School of Science, Xuchang University, Xuchang, China.
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, China.
Front Physiol. 2022 Jun 28;13:936982. doi: 10.3389/fphys.2022.936982. eCollection 2022.
Neuron modelling helps to understand the brain behavior through the interaction between neurons, but its mechanism remains unclear. In this paper, the spatiotemporal patterns is investigated in a general networked Hindmarsh-Rose (HR) model. The stability of the network-organized system without delay is analyzed to show the effect of the network on Turing instability through the Hurwitz criterion, and the conditions of Turing instability are obtained. Once the analysis of the zero-delayed system is completed, the critical value of the delay is derived to illustrate the profound impact of the given network on the collected behaviors. It is found that the difference between the collected current and the outgoing current plays a crucial role in neuronal activity, which can be used to explain the generation mechanism of the short-term memory. Finally, the numerical simulation is presented to verify the proposed theoretical results.
神经元建模有助于通过神经元之间的相互作用来理解大脑行为，但其机制仍不清楚。本文研究了一般网络化 Hindmarsh-Rose（HR）模型中的时空模式。通过Hurwitz准则分析了无延迟的网络组织系统的稳定性，以显示网络对图灵不稳定性的影响，并获得了图灵不稳定性的条件。一旦完成了零延迟系统的分析，就可以推导出延迟的临界值，以说明给定网络对所收集行为的深远影响。研究发现，收集到的电流与输出电流之间的差异在神经元活动中起着关键作用，这可用于解释短期记忆的产生机制。最后，进行了数值模拟以验证所提出的理论结果。
