Periodic Solutions of a Cohen-Grossberg-Type BAM Neural Networks with Distributed Delays and Impulses

A class of Cohen-Grossberg-type BAM neural networks with distributed delays and impulses are investigated in this paper. Sufficient conditions to guarantee the uniqueness and global exponential stability of the periodic solutions of such networks are established by using suitable Lyapunov function, the properties of 𝑀-matrix, and some suitable mathematical transformation. The results in this paper improve the earlier publications.

[1]  Jianhua Sun,et al.  Global exponential stability and periodic solutions of Cohen–Grossberg neural networks with continuously distributed delays , 2005 .

[2]  Chun-Hsien Li,et al.  Existence and attractivity of periodic solutions to non-autonomous Cohen–Grossberg neural networks with time delays , 2009 .

[3]  Jinde Cao,et al.  Periodic solutions and its exponential stability of reaction–diffusion recurrent neural networks with continuously distributed delays , 2006 .

[4]  Kelin Li,et al.  Stability in impulsive Cohen-Grossberg-type BAM neural networks with distributed delays , 2010, Appl. Math. Comput..

[5]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[6]  David H. Owens,et al.  Existence and learning of oscillations in recurrent neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[7]  Rui Xu,et al.  Periodic solutions of high-order Cohen–Grossberg neural networks with distributed delays , 2011 .

[8]  Jinde Cao,et al.  Exponential stability of periodic solution to Cohen-Grossberg-type BAM networks with time-varying delays , 2009, Neurocomputing.

[9]  Richard S. Varga,et al.  Matrix Iterative Analysis , 2000, The Mathematical Gazette.

[10]  José Carlos Príncipe,et al.  An analysis of the gamma memory in dynamic neural networks , 1994, IEEE Trans. Neural Networks.

[11]  Zhenkun Huang,et al.  Exponential periodic attractor of impulsive BAM networks with finite distributed delays , 2009 .

[12]  Kelin Li.  Stability analysis for impulsive Cohen–Grossberg neural networks with time-varying delays and distributed delays , 2009 .

[13]  Jinde Cao,et al.  Periodic bi-directional Cohen–Grossberg neural networks with distributed delays , 2007 .

[14]  Lu Zhao,et al.  Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales , 2009, Neurocomputing.

[16]  Xinsong Yang.  Existence and global exponential stability of periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks with delays and impulses , 2009, Neurocomputing.

[17]  Jiyu Wang,et al.  An analysis on the global exponential stability and the existence of periodic solutions for non-autonomous hybrid BAM neural networks with distributed delays and impulses , 2008, Comput. Math. Appl..

[18]  Xiaodi Li,et al.  Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays , 2009, Appl. Math. Comput..

[19]  Yongkun Li.  Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays , 2004 .