Stability and Hopf Bifurcation of Time Fractional Cohen–Grossberg Neural Networks with Diffusion and Time Delays in Leakage Terms

被引：0
作者：
Xiaohong Tian
Rui Xu
机构：
[1] Shijiazhuang Mechanical Engineering College,Institute of Applied Mathematics
来源：
Neural Processing Letters | 2017年 / 45卷
关键词：
Time fractional Cohen–Grossberg neural networks; Diffusion; Hopf bifurcation; Leakage delay; 39A11; 34K18; 92B20;
D O I：
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学科分类号：
摘要：
In this paper, a class of time fractional Cohen–Grossberg neural networks with time delays in leakage terms and diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation are established. By using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulae are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.
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页码：593 / 614
页数：21
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