Turing instability and pattern formation of neural networks with reaction–diffusion terms
Turing instability and pattern formation of neural networks with reaction–diffusion terms
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DOI：
10.1007/s11071-013-1114-2
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发表时间：
2013-10
影响因子：
5.6
通讯作者：
Hongyong Zhao;Xuanxuan Huang;Xuebing Zhang
中科院分区：
文献类型：
--
作者：
Hongyong Zhao;Xuanxuan Huang;Xuebing Zhang
本文研究了一种具有反应扩散的神经元网络模型。通过分析系统的线性稳定性，得到了系统的Hopf分岔条件和图灵不稳定条件。在此基础上，采用标准的多尺度分析方法推导了图灵分岔中激发态模型的振幅方程。此外，还确定了不同模式的稳定性。所得结果丰富了神经元网络系统的动力学。
In this paper, a model for a network of neurons with reaction–diffusion is investigated. By analyzing the linear stability of the system, Hopf bifurcation and Turing unstable conditions are obtained. Based on this, standard multiple-scale analysis is used for deriving the amplitude equations of the model for the excited modes in the Turing bifurcation. Moreover, the stability of different patterns is also determined. The obtained results enrich the dynamics of neurons’ network system.