AUTHOR=Zheng Qianqian , Shen Jianwei , Zhang Rui , Guan Linan , Xu Yong TITLE=Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model JOURNAL=Frontiers in Physiology VOLUME=13 YEAR=2022 URL=https://www.frontiersin.org/journals/physiology/articles/10.3389/fphys.2022.936982 DOI=10.3389/fphys.2022.936982 ISSN=1664-042X ABSTRACT=

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.