A Note on “Time Delays and Stimulus-Dependent Pattern Formation in Periodic Environments in Isolated Neurons’’

Journal of South China University of Technology (Natural Science Edition) ›› 2005, Vol. 33 ›› Issue (8): 45-48,61.

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A Note on “Time Delays and Stimulus-Dependent Pattern Formation in Periodic Environments in Isolated Neurons’’

Lao Yi-ping¹ Deng Fei-qi¹ Yang Feng-jian²

1.College of Automation Science and Engineering,South China Univ.of Tech.,Guangzhou 510640,Guangdong,China;2.Dept.of Mathematics,Zhongkai Agrotechnical College,Guangzhou 510225, Guangdong,China

Received:2005-01-04 Online:2005-08-25 Published:2005-08-25
Contact: 罗毅平(1966-)，博士生，主要从事神经网络的动力学性态、分布参数系统的控制和随机控制研究． E-mail:lyp8688@ sohu.corn
About author:罗毅平(1966-)，博士生，主要从事神经网络的动力学性态、分布参数系统的控制和随机控制研究．
Supported by:
国家自然科学基金资助项目(60374023)；广东省教育厅自然科学基金资助项目(Z0305A)；湖南省教育厅重点项目资助(A04012)

Abstract

Abstract:

A mistake in the proof of some technical problems in the literature as shown in the title of this paper is pointed out.By employing the continuous theorem of Mawhin’s coincidence degree theory and the Cauchv inequali-ty,sufficient conditions for the existence of the periodic solution to the model presented in the literatuIe are ob-tained.These sufi cient conditions are weaker than the ones in the existing literature.The unique and global attrac-tiveness of the periodic solution are then proved by employing Dini’s derivative. An example is finally presented to demonstrate the efectiveness of the proposed results.

Key words: neural network, periodic solution, continuous distributed time-delay, global attractiveness

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A Note on “Time Delays and Stimulus-Dependent Pattern Formation in Periodic Environments in Isolated Neurons’’

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