Bogdanov-Takens bifurcation in a neutral BAM neural networks model with delays
Bogdanov-Takens bifurcation in a neutral BAM neural networks model with delays
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具有延迟的中性 BAM 神经网络模型中的 Bogdanov-Takens 分岔
DOI：
10.1049/iet-syb.2017.0018
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发表时间：
2017
影响因子：
2.3
通讯作者：
Fang Yan
中科院分区：
文献类型：
--
作者：
Runxia Wang;Haihong Liu;Fei Feng;Fang Yan
本文首先讨论了具有两个时滞的五神经元中立型双向联想记忆神经网络模型的Bogdanov-Takens和三重零奇异性的存在性。然后，通过中心流形约化和选择适当的分支参数，得到了系统Bogdanov-Takens分支的二阶和三阶规范形.最后，所得到的规范形和数值模拟显示了一些有趣的现象，如存在一个稳定的不动点，一对稳定的非平凡平衡点，一个稳定的极限环，异宿轨道，同宿轨道，两个稳定的非平凡平衡点的共存和Bogdanov-Takens分歧临界点附近的稳定极限环。
In this study, the authors first discuss the existence of Bogdanov–Takens and triple zero singularity of a five neurons neutral bidirectional associative memory neural networks model with two delays. Then, by utilising the centre manifold reduction and choosing suitable bifurcation parameters, the second‐order and the third‐order normal forms of the Bogdanov–Takens bifurcation for the system are obtained. Finally, the obtained normal form and numerical simulations show some interesting phenomena such as the existence of a stable fixed point, a pair of stable non‐trivial equilibria, a stable limit cycles, heteroclinic orbits, homoclinic orbits, coexistence of two stable non‐trivial equilibria and a stable limit cycles in the neighbourhood of the Bogdanov–Takens bifurcation critical point.