Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model - Zheng, Qianqian; Shen, Jianwei; Zhang, Rui; Guan, Linan; Xu, Yong (Frontiers in Physiology, 2022)
Neuroscience is one of the most potential research field, especially the neuronal activities. In this paper, spatiotemporal patterns is investigated in a general networked Hindmarsh-Rose(HR) model. The stability of the network-organized system without delay is investigated to show the effect of network on pattern formation through Hurwitz criterion, and the conditions of Turing instability are obtained. Then, the critical value of delay is derived to illustrate a profound impact of network and delay on the collected behaviors. It is found that the difference between the collected current and the outgoing current plays a vital role in the 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.