Dynamics and control in an \(({\varvec{n}}+{\varvec{2}})\) -neuron BAM network with multiple delays
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- 作者：Chengdai Huang ; Jinde Cao ; Abdulaziz Alofi ; Abdullah AI-Mazrooei…
- 关键词：BAM network ; Stability ; Hopf bifurcation ; Time delay ; Bifurcating periodic solution
- 刊名：Nonlinear Dynamics
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：87
- 期：1
- 页码：313-336
- 全文大小：
- 刊物类别：Engineering
- 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
- 出版者：Springer Netherlands
- ISSN：1573-269X
- 卷排序：87
文摘
The issues of the stability and bifurcation for a delayed BAM network involving two neurons in the I-layer and arbitrary neurons in the J-layer are concerned in the present paper. By adopting the sum of the delays as the bifurcation parameter, we discuss the distribution of the roots of the characteristic equation for high-dimension system in terms of stability switches theory and further present some sufficient conditions for the occurrence of Hopf bifurcations. Analysis reveals that Hopf bifurcation will emerge after the given system loses its stability. Moreover, we derive explicit general formulae to determine the properties of bifurcation via the normal theory and the center manifold theorem. It is demonstrated that the sum of the delays can effectively affect the dynamics of the proposed system. Finally, an illustrative example is employed to verify the validity of the theoretical results obtained.