Spontaneous generation of spiral wave in the array of Hindmarsh-Rose neurons

作者：Peng Wang, Qianyun Li, Tang Guo-Ning · 发表于：Acta Physica Sinica · 年份：2018 · DOI：10.7498/aps.67.20172140 · 被引用次数：4 · 研究领域：Nonlinear Dynamics and Pattern Formation、stochastic dynamics and bifurcation、Neural dynamics and brain function

Spiral waves have been reported to be existent in the neocortex, during pharmacologically induced oscillations and sleep-like states. In the last decades, theoretical studies have demonstrated an underlying mechanism of the generation of spiral waves in a heart system. Nevertheless, how can a neural system produce spontaneous spiral wave and whether this behavior is sensitive to the dynamics of isolated neurons have not been systematically studied yet. In this paper we propose a modified Hindmarsh-Rose (HR) neuron model to study whether spiral wave can occur spontaneously in a two-dimensional array of HR neurons, which evolves from the initial state with a random phase distribution. The simulation results show that whether spiral wave can occur spontaneously in the system depends on the state of the single HR neuron, initial state of system and coupling strength. Especially, the state of the single HR neuron plays a central role. When the single HR neuron is in the state of period 1 spike, multiple spiral waves and spiral pairs can be generated spontaneously in the system for a certain range of coupling strength. In this case, the formations of spiral waves are completely independent of the initial state of the system, and as long as choosing an appropriate coupling strength, a single spiral wave can be found in the system. Furthermore, when the coupling strength exceeds a certain threshold value, the system will exhibit three kinds of dynamical behaviors, and correspond to t...