具有时变传输时滞的高阶Cohen-Grossberg型BAM神经网络的周期解
Periodic Solution for a Class of Higher-Order Cohen-Grossberg-Type BAM Neural Networks with Periodic Coefficients and Time-Varying Delays
DOI: 10.12677/AAM.2016.54095, PDF, HTML, XML, 下载: 2,021  浏览: 5,012  国家自然科学基金支持
作者: 田晓红, 徐瑞：军械工程学院基础部，河北 石家庄
关键词: 时变传输时滞；周期系数；周期解；全局稳定；Time-Varying Delays； Periodic Coefficients； Periodic Solution； Global Stability
摘要: 本文研究了具有周期系数和时变传输时滞的高阶Cohen-Grossberg型BAM神经网络，利用拓扑度中的Mawhin延拓定理，讨论了系统周期解的存在性，并通过构造适当的Lyapunov泛函，给出了周期解全局稳定的充分条件。
Abstract: A class of higher-order Cohen-Grossberg-type BAM neural networks with periodic coefficients and time-varying delays is studied in this paper. By using the continuation theorem of Mawhin’s coincidence degree theory, the existence of periodic solutions of networks is discussed, and by constructing appropriate Lyapunov functional, sufficient conditions are established for the global stability of the periodic solution.
文章引用：田晓红, 徐瑞. 具有时变传输时滞的高阶Cohen-Grossberg型BAM神经网络的周期解[J]. 应用数学进展, 2016, 5(4): 823-835. http://dx.doi.org/10.12677/AAM.2016.54095

参考文献

[1] 王阿明, 刘天放, 王绪. 高阶神经网络模型特性研究[J]. 中国矿业大学学报, 2003, 32(2): 177-179.
[2] Chen, Z., Zhao, D. and Ruan, J. (2007) Dynamic Analysis of High-Order Cohen-Grossberg Neural Networks with Time Delay. Chaos, Solitons & Fractals, 32, 1538-1546.
https://doi.org/10.1016/j.chaos.2005.11.095
[3] Ke, Y. and Miao, C. (2011) Periodic Solutions for High-Order Cohen-Grossberg-Type BAM Neural Networks with Time-Delays. Advances in Neural Networks, 6675, 375-384.
https://doi.org/10.1007/978-3-642-21105-8_44
[4] Ren, F. and Cao, J. (2007) Periodic Oscillation of Higher-Order Bidirectional Associative Memory Neural Networks with Periodic Coefficients and Delays. Nonlinearity, 20, 605-629.
https://doi.org/10.1088/0951-7715/20/3/004
[5] 王林山. 时滞递归神经网络[M]. 北京: 科学出版社, 2008.
[6] 许天周. 应用泛函分析[M]. 北京: 科学出版社, 2001.
[7] 郭大钧, 孙经先, 刘兆理. 非线性常微分方程泛函方法[M]. 济南: 山东科学技术出版社, 2005.
[8] Gaines, R. and Mawhin, J. (1977) Coincidence Degree, and Nonlinear Differential Equations. Springer-Verlag, Berlin.
https://doi.org/10.1007/BFb0089537
[9] 陈景良, 陈向晖. 特殊矩阵[M]. 北京: 清华大学出版社, 2001.
[10] Gopalsamy, K. (1992) Stability and Oscillation in Delay Equation of Population Dynamics. Kluwer Academic Publishers, Dordreeht.

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