Dynamical Behavior Analysis of a Class of Complex-Valued Neural Networks With Time-Varying Delays

XU Xiao-hui; SONG Qian-kun; ZHANG Ji-ye; SHI Ji-zhong; ZHAO Ling.

doi:10.21656/1000-0887.380015

Volume 38 Issue 12

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Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(12): 1389-1398

XU Xiao-hui, SONG Qian-kun, ZHANG Ji-ye, SHI Ji-zhong, ZHAO Ling.. Dynamical Behavior Analysis of a Class of Complex-Valued Neural Networks With Time-Varying Delays[J]. Applied Mathematics and Mechanics, 2017, 38(12): 1389-1398. doi: 10.21656/1000-0887.380015

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Dynamical Behavior Analysis of a Class of Complex-Valued Neural Networks With Time-Varying Delays

doi: 10.21656/1000-0887.380015

¹Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu 610039, P.R.China;²Key Laboratory of Automobile Measurement and Control & Safety, Xihua University, Chengdu 610039, P.R.China;³College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China;⁴State Key Laboratory of Traction Power(Southwest Jiaotong University),Chengdu 610031, P.R.China;⁵College of Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, P.R.China

Funds: The National Natural Science Foundation of China（11402214;51375402;11572264;61773004）

Received Date: 2017-01-11
Rev Recd Date: 2017-11-02
Publish Date: 2017-12-15

Abstract

Abstract

The dynamical behavior of a class of complex-valued Cohen-Grossberg neural networks with time-varying delays was studied. It was supposed that the activation functions satisfied the Lipschitz condition and the amplification functions had only the lower bounds. The sufficient conditions ensuring the existence and the uniqueness of the equilibrium point of the system were acquired by means of the M matrix and the homeomorphic mapping. Furthermore, based on the vector Lyapunov function method and the inequality technique the criteria were obtained to judge the mode exponential stability of the equilibrium point of the system. The form of the obtained sufficient conditions is simple, and is easy to be verified in practice. The presented results generalize the existing ones. Finally a numerical example through simulation was given to verify the correctness and feasibility of the obtained results.
- Cohen-Grossberg neural network,
- complex-valued domain,
- mode stability,
- exponential stability,
- time-varying delay,
- vector Lyapunov function method

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References(18)

References

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