Stability of Impulsive Disturbance Complex-Valued Cohen-Grossberg Neural Networks in a Complex Number Domain

被引：0
|
作者：
Xu X. [1 ,2 ]
Xu Q. [3 ]
Shi J. [4 ]
Zhang J. [5 ]
Chen Z. [1 ]
机构：
[1] Key Laboratory of Automobile Measurement and Control & Safty, Xihua University, Chengdu
[2] Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu
[3] School of Technology, Xihua University, Chengdu
[4] College of Engineering, Zhejiang Normal University, Jinhua
[5] National Traction Power Laboratory, Southwest Jiaotong University, Chengdu
来源：
Xu, Quan (quanxnjd@sina.com) | 2018年 / Science Press卷 / 53期
关键词：
Cohen-Grossberg neural networks; Complex number domain; Exponential stability; Impulsive disturbances; Lyapunov function; Time-varying delays;
D O I：
10.3969/j.issn.0258-2724.2018.04.021
中图分类号：
学科分类号：
摘要：
To analyse the effect of impulsive disturbances on neural networks, the dynamical behaviour of these disturbances was examined at the module of the equilibrium point of a class of complex-valued Cohen-Grossberg neural networks with time-varying delays. It was assumed that amplification, self-feedback, and activation functions were defined in a complex number domain. First, the existence and uniqueness of the equilibrium point of the system were analysed by utilising the corresponding property of the M matrix and the theorem of homeomorphism mapping. Second, the globally exponential stability of the module of the equilibrium point of the system was studied by applying the vector Lyapunov function and mathematical induction methods. The corresponding stability criteria were then established. Finally, two numerical examples from simulations were given to illustrate the practicability and correctness of the obtained results. The simulation results revealed that the states of the addressed system can reach equilibrium within 0.5 s. Other results showed that the greater the delay and impulsive strength and the smaller the amplification, the slower was the state convergence rate. © 2018, Editorial Department of Journal of Southwest Jiaotong University. All right reserved.
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页码：820 / 828
页数：8
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