一类四维时滞前馈神经网络模型的Hopf分支  

Hopf Bifurcation of a Four-Dimensional Feed-forward Neural Network Model with Time Delay

作　　者：王殿宏 王文龙[1] 李雪 WANG Dianhong;WANG Wenlong;LI Xue(Department of Mathematic,Northeast Forestry University,Harbin 150040,China)

机构地区：[1]东北林业大学数学系,哈尔滨150040

出　　处：《湖北民族大学学报（自然科学版）》2020年第1期32-37,共6页Journal of Hubei Minzu University:Natural Science Edition

基　　金：中央高校基本科研业务费专项资金资助项目(DL13BB17);东北林业大学大学生创新训练计划项目(201810225096).

摘　　要：研究一类四维时滞前馈神经网络模型,讨论了系统产生Hopf分支的条件;利用中心流形定理和规范型理论,针对系统在平衡点处出现Hopf分支的情形,给出了模型的规范型,并且研究了Hopf分支周期解的稳定性及分支方向;最后,给出了数值仿真模拟验证.The four-dimensional feed-forward neural network model with time delay is investigated,and the conditions for generating Hopf bifurcation are discussed.Using the central manifold theorem and the normal form theory,for the case of Hopf bifurcation at the equilibrium point,we compute the normal form of the model and derive the explicit formulae for determining the direction of the bifurcation and the stability of the bifurcating periodic solutions.Finally,the numerical simulation is given.

关 键 词：神经网络 时滞 HOPF分支 规范型 周期解 

分 类 号：O175[理学—数学]