A Novel Approach to Positive Almost Periodic Solution of BAM Neural Networks with Time-Varying Delays

In this paper, based on almost periodic functional hull theory and M-matrix theory, some sufficient conditions are established for the existence and uniqueness of positive almost periodic solution for a class of BAM neural networks with time-varying delays. An example is given to illustrate the main results.


Authors:



References:
[1] H. Zhao, Global stability of bidirectional associative memory neural
networks with distributed delays, Phys. Lett. A 297 (2002) 182-190.
[2] J. Liang, J. Cao, Global asymptotic stability of bi-directional associative
memory networks with distributed delays, Appl. Math. Comput. 152
(2004) 415-424.
[3] R. Samidurai, R. Sakthivel, S.M. Anthoni, Global asymptotic stability
of BAM neural networks with mixed delays and impulses, Appl. Math.
Comput. 212 (2009) 113-119.
[4] Y. Li, Global exponential stability of BAM neural networks with delays
and impulses, Chaos, Solitons and Fractals 24 (2005) 279-285.
[5] Y. Liu, W. Tang, Existence and exponential stability of periodic solution
for BAM neural networks with periodic coefficients and delays, Neurocomputing,
69 (2006) 2152-2160.
[6] J. Cao, Periodic oscillatory solution of bidirectional associative memory
networks with delays, Phys. Rev. E 61 (2000) 1825-1828.
[7] Y. Li, Existence and stability of periodic solution for BAM neural
networks with distributed delays, Appl. Math. Comput. 159 (2004) 847-
862.
[8] A. Chen, L. Huang, J. Cao, Existence and stability of almost periodic
solution for BAM neural networks with delays, Appl. Math. Comput.
137 (2003) 177-193.
[9] Y. Xia, J. Cao, M. Lin, New resule on the existence and uniqueness
of almost periodic solution for BAM neural networks with continuously
distributed delays, Chaos Solitons Fract. 31 (2007) 928-936.
[10] C. He, almost periodic differential equations, Higher Education Publishing
House, Beijing, 1992(in Chinese).
[11] H. Tokumarn, N. Adachi, T. Amemiya, Macroscopic stability of interconnected
systems, in: Proceedings of the 6th IFAC Congress, Paper
ID44.4, 1975.