Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model

Qianqian Zheng; Jianwei Shen; Rui Zhang; Linan Guan; Yong Xu

doi:10.3389/fphys.2022.936982

Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model

Front Physiol. 2022 Jun 28:13:936982. doi: 10.3389/fphys.2022.936982. eCollection 2022.

Authors

Qianqian Zheng¹, Jianwei Shen², Rui Zhang³, Linan Guan², Yong Xu⁴

Affiliations

¹ School of Science, Xuchang University, Xuchang, China.
² School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, China.
³ School of Mathematics, Northwest University, Xi'an, China.
⁴ School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, China.

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.

Keywords: HR model; delay; matrix; network; pattern formation; turing instability.