Existence of Periodic Solution for Hopfield Cellular Neural Networks

As an important tool to study practical problems of biology, engineering and image processing, the cellular neural networks (CNNs) has caused more and more attention. Some interesting results about the existence for cellular neural networks have been obtained. In this paper, by means of iterative analysis, the existence of periodic solution for Hopfield cellular neural networks are considered. Some new results are obtained.

[1]  Valeri Mladenov,et al.  Cellular Neural Networks: Theory And Applications , 2004 .

[2]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[3]  Yongkun Li,et al.  Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses , 2004 .

[4]  Juan J. Nieto,et al.  Periodic boundary value problems for a class of functional differential equations , 1996 .

[5]  J. Nieto,et al.  Impulsive periodic boundary value problems of first-order differential equations , 2007 .

[6]  Chuanzhi Bai,et al.  Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying delays , 2008, Appl. Math. Comput..

[7]  Jinde Cao New results concerning exponential stability and periodic solutions of delayed cellular neural networks , 2003 .

[8]  Dajun Guo,et al.  Periodic boundary value problems for second order impulsive integro-differential equations in Banach spaces , 1997 .

[9]  Tamás Roska,et al.  Image compression by cellular neural networks , 1998 .

[10]  Zhimin He,et al.  Periodic boundary value problem for first-order impulsive functional differential equations , 2002 .

[11]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[12]  H. Akça,et al.  Continuous-time additive Hopfield-type neural networks with impulses , 2004 .

[13]  Guanrong Chen,et al.  On delayed impulsive Hopfield neural networks , 1999, Neural Networks.

[14]  Zhigang Zeng,et al.  Global asymptotic stability and global exponential stability of delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  Zhang,et al.  EXISTENCE FOR PERIODIC BOUNDARY VALUE PROBLEM OF FIRST-ORDER INTEGRO-DIFFERENTIAL EQUATIONS , 2007 .

[16]  K. Gopalsamy,et al.  Stability of artificial neural networks with impulses , 2004, Appl. Math. Comput..

[17]  Tianping Chen,et al.  Robust global exponential stability of Cohen-Grossberg neural networks with time delays , 2004, IEEE Transactions on Neural Networks.

[18]  Jinde Cao,et al.  Stability and periodicity in delayed cellular neural networks with impulsive effects , 2007 .

[19]  Zhi-Hong Guan,et al.  On impulsive autoassociative neural networks , 2000, Neural Networks.

[20]  Tamás Roska,et al.  Image compression by cellular neural networks , 1998 .

[21]  Xiaoming He,et al.  Periodic boundary value problems for first order impulsive integro-differential equations of mixed type , 2004 .

[22]  Liao Xiao-Xin Mathematical theory of cellular neural networks (II) , 1995 .

[23]  Jinde Cao,et al.  Periodic solutions and exponential stability in delayed cellular neural networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Juan J. Nieto,et al.  Basic Theory for Nonresonance Impulsive Periodic Problems of First Order , 1997 .

[25]  Huaguang Zhang,et al.  LMI Approach to Robust Stability Analysis of Cohen-Grossberg Neural Networks with Multiple Delays , 2006, ISNN.

[26]  Guan Huan-xin,et al.  New Criteria for Robust Stability of Cohen-Grossberg Neural Networks with Multiple Delays , 2007 .

[27]  Yonghui Xia,et al.  Existence and exponential stability of almost periodic solution for Hopfield-type neural networks with impulse , 2008 .

[28]  Wei Ding,et al.  Periodic boundary value problems for the first order impulsive functional differential equations , 2005, Appl. Math. Comput..