文献类型：期刊文献

中文题名：Stability switches and bifurcation analysis in a coupled neural system with multiple delays

英文题名：Stability switches and bifurcation analysis in a coupled neural system with multiple delays

作者：Ge JuHong[1];Xu Jian[2]

第一作者：Ge JuHong

通讯作者：Ge, JH[1]

机构：[1]Henan Univ Econ & Law, Dept Math & Informat Sci, Zhengzhou 450046, Peoples R China;[2]Tongji Univ, Sch Aerosp Engn & Appl Mech, Shanghai 200092, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Henan Univ Econ & Law, Dept Math & Informat Sci, Zhengzhou 450046, Peoples R China.|[1048425]河南财经政法大学数学与信息科学学院;[10484]河南财经政法大学;

年份：2016

卷号：0

期号：6

起止页码：920-931

中文期刊名：中国科学：技术科学英文版

外文期刊名：SCIENCE CHINA-TECHNOLOGICAL SCIENCES

收录：;EI(收录号：20161302174916);Scopus(收录号：2-s2.0-84961616447);WOS:【SCI-EXPANDED(收录号:WOS:000376653300010)】；CSCD:【CSCD2015_2016】；

基金：This work was supported by the National Natural Science Foundation of China (Grant Nos. 11202068 & 11572224), the University Key Teacher Foundation for Youths of Henan Province (Grant No. 2014GGJS-076), and the Key Technologies Research Project of Henan Province (Grant No. 152102210089).

语种：英文

中文关键词：局部渐近稳定性;神经系统;多时滞;耦合;分岔分析;开关;平衡点;稳定性判据

外文关键词：multiple delays; stability switches; global stability

摘要：A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the pitchfork bifurcation of the trivial equilibrium point. Further, the local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independent and delay-dependent stability. Increasing delay induces stability switching between resting state and periodic motion in some parameter regions of coupling weight. In addition, the criterion for the global stability of the trivial equilibrium is also derived by constructing a suitable Lyapunov functional. Finally, some numerical simulations are taken to support the theoretical results.
A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the pitchfork bifurcation of the trivial equilibrium point. Further, the local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independent and delay-dependent stability. Increasing delay induces stability switching between resting state and periodic motion in some parameter regions of coupling weight. In addition, the criterion for the global stability of the trivial equilibrium is also derived by constructing a suitable Lyapunov functional. Finally, some numerical simulations are taken to support the theoretical results.