Bifurcation analysis in a neutral BAM neural network model with delays

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• 英文论文题名：Bifurcation analysis in a neutral BAM neural network model with delays
• 论文作者：Runxia Wang ; Haihong Liu ; Fang Yan
• 英文论文作者：Runxia Wang ; Haihong Liu ; Fang Yan ; Department of Mathematical ; Yunnan Normal University
• 年：2016
• 作者机构：Department of Mathematical, Yunnan Normal University;
• 英文论文关键词：Neural type ; BAM neural network ; Hopf bifurcation ; Hopf-pitchfork bifurcation ; Periodic solution
• 会议召开时间：2016-05-06
• 会议录名称：第十届动力学与控制学术会议摘要集
• 语种：英文
• 分类号：TP183
• 学会代码：AGLU
• 会议名称：第十届动力学与控制学术会议
• 会议地点：中国四川成都
• 主办单位：中国力学学会动力学与控制专业委员会
• 学会名称：中国力学学会
• 页数：2
• 文件大小：600k
• 原文格式：D
• 会议级别：全国

摘要

In this paper, we study the dynamical behaviors of a four-neurons neutral BAM neural networks with two delays. By studying the distribution of the eigenvalues of the associated characteristic equation, we drive the critical values where Hopf and Hopf-pitchfork bifurcation occur. Then, the stability and direction of Hopf bifurcation, and normal form of Hopf-pitchfork are obtained by applying center manifold theorem and normal form method. Moreover, we find some interesting phenomenas, such as the existence of a stable fixed point, a pair of stable fixed points, a stable periodic solution, and co-existence of a pair of stable periodic solutions in the neighborhood of the Hopf-pitchfork critical point, which are all illustrated both theoretically and numerically.
In this paper, we study the dynamical behaviors of a four-neurons neutral BAM neural networks with two delays. By studying the distribution of the eigenvalues of the associated characteristic equation, we drive the critical values where Hopf and Hopf-pitchfork bifurcation occur. Then, the stability and direction of Hopf bifurcation, and normal form of Hopf-pitchfork are obtained by applying center manifold theorem and normal form method. Moreover, we find some interesting phenomenas, such as the existence of a stable fixed point, a pair of stable fixed points, a stable periodic solution, and co-existence of a pair of stable periodic solutions in the neighborhood of the Hopf-pitchfork critical point, which are all illustrated both theoretically and numerically.

引文