Browse > Article
http://dx.doi.org/10.14317/jami.2013.577

GLOBAL EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS OF HIGH-ORDER HOPFIELD NEURAL NETWORKS WITH DISTRIBUTED DELAYS OF NEUTRAL TYPE  

Zhao, Lili (Department of Mathematics, Yunnan University)
Li, Yongkun (Department of Mathematics, Yunnan University)
Publication Information
Journal of applied mathematics & informatics / v.31, no.3_4, 2013 , pp. 577-594 More about this Journal
Abstract
In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.
Keywords
High-order Hopfield neural networks; neutral distributed delays; almost periodic solution; Global exponential stability; fixed point theorem;
Citations & Related Records
연도 인용수 순위
  • Reference
1 B. Xiao and H Meng, Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks, Appl. Math. Modelling 33 (2009), 532-542.   DOI   ScienceOn
2 Y. Yu and M. Cai, Existence and exponential stability of almost-periodic solutions for high-order Hopfield neural networks, Math. Comput. Modelling 47 (2008), 943-951.   DOI   ScienceOn
3 B. Xu, X. Liu and X. Liao, Global exponential stability of high order Hopfield type neural networks, Appl. Math. Comput. 174 (2006), 98-116.   DOI   ScienceOn
4 C.Z. Bai, Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying delays, Appl. Math. Comput. 203 (2008), 72-79.   DOI   ScienceOn
5 B. Xu, X. Liu and K.L. Teo, Global exponential stability of impulsive high-order Hopfield type neural networks with delays, Comput. Math. Appl. 57 (2009), 1959-1967.   DOI   ScienceOn
6 P. Shi and L. Dong, Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses, Appl. Math. Comput. 216 (2010), 623-630.   DOI   ScienceOn
7 J. Li, J. Yang and W. Wu, Stability and periodicity of discrete Hopfield neural networks with column arbitrary-magnitude-dominant weight matrix, Neurocomputing 82 (2012), 52-61.   DOI   ScienceOn
8 J.H. Park, O.M. Kwon and S.M. Lee, LMI optimization approach on stability for delayed neural networks of neutral-type, Appl. Math. Comput. 196 (2008), 236-244.   DOI   ScienceOn
9 J.H. Park, C.H. Park, O.M. Kwon and S.M. Lee, A new stability criterion for bidirectional associative memory neural networks of neutral-type, Appl. Math. Comput. 199 (2008) 716-722.   DOI   ScienceOn
10 S.M. Lee, O.M. Kwon and J.H. Park, A novel delay-dependent criterion for delayed neural networks of neutral type, Phys. Lett. A 374 (2010), 1843-1848.   DOI   ScienceOn
11 Y.K. Li, L. Zhao and P. Liu, Existence and exponential stability of periodic solution of high-order Hopfield neural network with delays on time scales, Discrete Dyamics in Nature and Society 2009 (2009), Article ID573534, 18pages.
12 A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, vol. 377, Springer, Berlin, 1974.
13 S. Mohamad, Exponential stability in Hopfield-type neural networks with impuses, Chaos Solitons Fractals 32 (2007), 456-467.   DOI   ScienceOn
14 B. J. Xu and X. Z. Liu, Global asymptotic stability of high-order Hopfield type neurual networks with time delays, Comput. Math. Appl. 45 (2003), 1279-1737.
15 E.B. Kosmatopoulos and M.A. Christodoulou, Structural properties of gradient recurrent high-order neural networks, IEEE Trans. Circuits Syst. II 42 (1995), 592-603.   DOI   ScienceOn
16 Y.K. Li, L. Zhao and X.R. Chen, Existence of periodic solutions for neutral type cellular neural networks with delays, Appl. Math. Modelling 36 (2012), 1173-1183.   DOI   ScienceOn
17 S. Mandal and N.C. Majee, Existence of periodic solutions for a class of Cohen-Grossberg type neural networks with neutral delays, Neurocomputing 74 (2011), 1000-1007.   DOI   ScienceOn
18 K. Wang and Y. Zhu, Stability of almost periodic solution for a generalized neutral-type neural networks with delays, Neurocomputing 73 (2010), 3300-3307.   DOI   ScienceOn
19 S. Mandal and N.C. Majee, Existence of periodic solutions for a class of Cohen-Grossberg type neural networks with neutral delays, Neurocomputing 74 (2011), 1000-1007.   DOI   ScienceOn
20 C. Y. He, Almost Periodic Differential Equations, Higher Education Publishing House, Beijing, 1992 (in Chinese).
21 X. Lou and B. Cui, Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays, J. Math. Anal. Appl. 330 (2007), 144-158.   DOI   ScienceOn