脉冲时滞细胞神经网络周期解的存在性和指数稳定性

重庆交通大学学报（自然科学版） ›› 2010, Vol. 29 ›› Issue (2): 321-325.

脉冲时滞细胞神经网络周期解的存在性和指数稳定性

李中华¹，王慧²

1.乐山师范学院计算机科学学院，四川乐山 614004 ; 2.乐山师范学院数学与信息科学学院，四川乐山 614004

收稿日期:2009-10-19 修回日期:2009-11-16 出版日期:2010-04-15 发布日期:2015-01-22
作者简介:李中华(1974—)，男，四川眉山人，讲师，硕士，主要从事网络与数据库方面的研究工作。E-mail:lslizhonghua@163.com。
基金资助:
中国博士后科学基金项目(20080431274)

Periodic Solutions of Cellular Neural Networks with Impulses and Delays

LI Zhong-hua¹，WANG Hui²

1.Department of Computer，Leshan Normal University，Leshan 614004，Sichuan，China; 2.Department of Math，Leshan Normal University，Leshan614004，Sichuan，China

Received:2009-10-19 Revised:2009-11-16 Online:2010-04-15 Published:2015-01-22

摘要/Abstract

摘要： 研究了脉冲时滞神经网络周期解的存在性和全局指数稳定性问题。运用控制压缩原理和Lyapunov函数建立了几个确保系统周期解存在和稳定的充分条件。有助于设计和应用CNN型生物和人工神经网络。数值实例验证了结论的正确性。

关键词: 细胞神经网络, 周期解, 指数稳定性

Abstract: A celluar neural network(CNN) with impulses and time － delay is studied. With less conservative，some new sufficient conditions for the existence and global exponential stability of periodic solution are established. It is believed that these results are significant and useful for the design and applications of CNN-type biological and artificial neural networks.

Key words: cellular neural networks (CNNs), periodic solution, exponential stability

中图分类号:

TP183

李中华，王慧. 脉冲时滞细胞神经网络周期解的存在性和指数稳定性[J]. 重庆交通大学学报（自然科学版）, 2010, 29(2): 321-325.

LI Zhong-hua，WANG Hui. Periodic Solutions of Cellular Neural Networks with Impulses and Delays[J]. Journal of Chongqing Jiaotong University(Natural Science), 2010, 29(2): 321-325.

参考文献

[1] Chua L O，Yang L. Cellular neural networks: theory [J]. IEEE Trans. Circuits Systems，1988，35(10): 1257 － 1272.
[2] Chua L O，Yang L. Cellular neural networks: application [J].IEEE Transactions on Circuits and Systems，1988，35(10): 1273－ 1290.
[3] Cao J，Chen T. Globally exponentially robust stability and periodicity of delayed neural networks [J]. Chaos，Solitons and Fractals，2004，22(4): 957 – 963.
[4] Cao J，Wang J. Global exponential stability and periodicity of recurrent neural networks with time delays [J]. IEEE Trans. Circ.Syst. I，2005，52(5): 920 – 931
[5] Delgado A，Kambhampati C，Warwick K. Input /output linearization using dynamic recurrent neural networks[J]. Math. Comput.Simul，1996，41(5 /6): 451 – 460.
[6] Hopfield J J. Neural networks and physical systems with emergent collective computational abilities[J]. Proc. Natl. Acad. Sci，1982，79(2): 2554 – 2558.
[7] Sun C，Feng C. Exponential periodicity and stability of delayed neural networks [J]. Math. Comput. Simul，2004，66(6): 469– 478.
[8] Zhao H. Global exponential stability and periodicity of cellular neural networks with variable delays[J ]. Physics Letters A，2005，336(4 /5): 331 – 341.
[9] Dong M. Global exponential stability and existence of periodic solutions of CNNs with delays[J]. Physics Letters A，2002，300(1):49 – 57.
[10] Liu B，Huang L. Existence of periodic solutions for cellular neural networks with complex deviating arguments [J ]. Applied Mathematics Letters，2007，20(1):103 – 109.
[11] Li Y，Zhu L，Liu P. Existence and stability of periodic solutions of delayed cellular neural networks [J]. Nonlinear Analysis: RealWorld Applications，2006，7(2):225 – 234.
[12] Liu Z，Liao L. Existence and global exponential stability of periodic solution of cellular neural networks with time － varying delays[J]. J. Math. Anal. Appl. ，2004，290(1):247 – 262.
[13] Zhou J，Liu Z，Chen G. Dynamics of periodic delayed neural networks[J]. Neural Networks，2004，17(1):87 – 101
[14] Liu B，Huang L. Existence and exponential stability of almost periodic solutions for cellular neural networks with mixed delays [J]. Chaos，Solitons and Fractals，2007，32(1):95 – 103.
[15] Gui Z，Ge W. Existence and uniqueness of periodic solutions of nonautonomous cellular neural networks with impulses [J]. Physics Letters A，2006，354(1 /2): 84 –94.