Browse > Article
http://dx.doi.org/10.14317/jami.2012.30.5_6.1051

EXISTENCE AND STABILITY OF ALMOST PERIODIC SOLUTIONS FOR A CLASS OF GENERALIZED HOPFIELD NEURAL NETWORKS WITH TIME-VARYING NEUTRAL DELAYS  

Yang, Wengui (Ministry of Public Education, Sanmenxia Polytechnic)
Publication Information
Journal of applied mathematics & informatics / v.30, no.5_6, 2012 , pp. 1051-1065 More about this Journal
Abstract
In this paper, the global stability and almost periodicity are investigated for generalized Hopfield neural networks with time-varying neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results. Finally, an example is given to demonstrate the effectiveness of our results.
Keywords
Hopfield neural networks; time-varying neutral delays; almost periodic solutions; exponential stability; fixed point theorem;
Citations & Related Records
연도 인용수 순위
  • Reference
1 O.M. Kwon, J.H. Park, S.M. Lee, On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays, Appl. Math. Comput. 197 (2008), 864-873.
2 J.H. Park, O.M. Kwon, LMI optimization approach on stability for delayed neural networks of neutral-type, Appl. Math. Comput. 196 (2008), 236-244.
3 B. Xiao, Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays, Appl. Math. Lett. 22 (2009), 528-533.   DOI
4 A.M. Fink, Almost Periodic Differential Equations, in: Lecture Notes in Mathematics, vol. 377, Springer, Berlin, 1974, pp. 80-112.
5 C.Y. He, Almost Periodic Differential Equation, Higher Education Publishing House, Beijing, 1992, pp. 90-100 (in Chinese).
6 P. Shi, L. Dong, Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses, Appl. Math. Comput. 216 (2010), 623-630.
7 L. Huang, J.Wang, X. Zhou, Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations, Nonlinear Anal. RWA 10 (2009), 1651-1661.   DOI
8 C. Bai, Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays, Nonlinear Anal. TMA 71 (2009), 5850-5859.   DOI
9 J. Cao, A. Chen, X. Huang, Almost periodic attraction of delayed neural networks with variable coefficients, Phys. Lett. A 340 (2005), 104-120.   DOI
10 R. Rakkiyappan, P. Balasubramaniam, J. Cao, Global exponential stability results for neutral-type impulsive neural networks, Nonlinear Anal. RWA 11 (2010), 122-130.   DOI
11 P. Balasubramaniam, S. Lakshmanan, Delay-range dependent stability criteria for neural networks with Markovian jumping parameters, Nonlinear Anal. Hybrid Syst. 3 (4) (2009), 749-756.   DOI
12 S. Lakshmanan, P. Balasubramaniam, New results of robust stability analysis for neutral type neural networks with time-varying delays and Markovian jumping parameters, Canad. J. Phys. 89 (2011), 827-840 .   DOI
13 Z. Wang, Y. Liu, X. Liu, On global asymptotic stability of neural networks with discrete and distributed delays, Phys. Lett. A 345 (2005), 299-308.   DOI
14 Z. Wang et al., The existence and uniqueness of periodic solutions for a kind of Duffingtype equation with two deviating arguments, Nonlinear Anal. TMA 73 (2010), 3034-3043.   DOI
15 G. Wang, J. Cao, L. Wang, Global dissipativity of stochastic neural networks with time delay, J. Franklin Inst. 346 (2009) 794-807.   DOI
16 J. Qiu, J. Cao, Delay-dependent exponential stability for a class of neural networks with time delays and reaction-diffusion terms, J. Franklin Inst. 346 (2009), 301-314.   DOI
17 G.T. Stamov, I.M. Stamova, Almost periodic solutions for impulsive neural networks with delay, Appl. Math. Model. 31 (2007), 1263-1270.   DOI
18 I.M. Stamova, G.T. Stamov, Impulsive control on global asymptotic stability for a class of impulsive bidirectional associative memory neural networks with distributed delays, Math. Comput. Model. 53 (2011), 824-831.   DOI
19 S. Mohamad, Exponential stability in Hopfield-type neural networks with impulses, Chaos Solitons Fractals 32 (2007), 456-467.   DOI
20 Z. Huang, S. Mohamad, C. Feng, New results on exponential attractivity of multiple almost periodic solutions of cellular neural networks with time-varying delays, Math. Comput. Model. 52 (2010), 1521-1531.   DOI
21 S. Mohamad, K. Gopalsamy, H. Akca, Exponential stability of artificial neural networks with distributed delays and large impulses, Nonlinear Anal. RWA 9 (2008), 872-888.   DOI
22 J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. USA 79 (1982), 2554-2558.   DOI
23 J. Hopfield, Neurons with graded response have collective computational properties like those of two-stage neurons, Proc. Natl. Acad. Sci. USA 81 (1984), 3088-3092.   DOI
24 B. Liu, L. Huang, Existence and exponential stability of almost periodic solutions for Hopfield neural networks with delays, Neurocomputing 68 (2005), 196-207.   DOI
25 Z. Gui, W. Ge, X. Yang, Periodic oscillation for a Hopfield neural networks with neutral delays, Phys. Lett. A 364 (2007), 267-273.   DOI
26 Q. Dong, K. Matsui, X. Haung, Existence and stability of periodic solutions for Hopfield neural network equations with periodic input, Nonlinear Anal. TMA 49 (2002), 471-479.   DOI
27 X. Li, Z. Chen, Stability properties for Hopfield neural networks with delays and impulsive perturbations, Nonlinear Anal. RWA 10 (2009), 3253-3265.   DOI
28 X. Fu, X. Li, Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays, J. Comput. Appl. Math. 231 (2009), 187-199.   DOI
29 H. Zhao, Global asymptotic stability of Hopfield neural network involving distributed delays, Neural Networks 17 (2004), 47-53.   DOI