Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays

Nonlinear Analysis, Theory, Methods and Applications

Volumn 71, Issue 11, 2009, Pages 5850-5859

  Bai, Chuanzhi ^a  

^a HUAIYIN NORMAL UNIVERSITY   (China)

Author keywords

Almost periodic solution; Continuously distributed delays; Exponential stability; Fixed point theorem; Hopfield neural networks

Indexed keywords

ALMOST PERIODIC SOLUTION; ALMOST PERIODIC SOLUTIONS; ALMOST PERIODICITY; CONTINUOUSLY DISTRIBUTED DELAYS; DIFFERENTIAL INEQUALITY TECHNIQUES; EXISTENCE AND STABILITY; EXPONENTIAL STABILITY; FIXED POINT THEOREM; FIXED POINT THEOREMS; GLOBAL STABILITY; GLOBALLY EXPONENTIAL STABILITY; NEUTRAL DELAYS; SUFFICIENT CONDITIONS;

DIFFERENTIAL EQUATIONS; NEURAL NETWORKS; STABILITY;

HOPFIELD NEURAL NETWORKS;

EID: 68349105795     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.05.008     Document Type: Article

References (19)

1. Hopfield J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79 (1982) 2554-2558
2. Hopfield J. Neurons with graded response have collective computational properties like those of two-stage neurons. Proc. Natl. Acad. Sci. USA 81 (1984) 3088-3092
3. Cao J. New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys. Lett. A 307 (2003) 136-147
4. Cao J., Chen A., and Huang X. Almost periodic attraction of delayed neural networks with variable coefficients. Phys. Lett. A 340 (2005) 104-120
5. Dong Q., Matsui K., and Haung X. Existence and stability of periodic solutions for Hopfield neural network equations with periodic input. Nonlinear Anal. 49 (2002) 471-479
6. Gui Z., Ge W., and Yang X. Periodic oscillation for a Hopfield neural networks with neutral delays. Phys. Lett. A 364 (2007) 267-273
7. Guo S., and Huang L. Periodic solutions in an inhibitory two-neuron network. J. Comput. Appl. Math. 161 (2003) 217-229
8. Guo S., and Huang L. Stability analysis of a delayed Hopfield neutral network. Phys. Rev. E 67 (2003) 1-7
9. Huang H., Cao J., and Wang J. Global exponential stability and periodic solutions of recurrent cellular neural networks with delays. Phys. Lett. A 298 (2002) 393-404
10. Liu B., and Huang L. Existence and global exponential stability of almost periodic solutions for Hopfield neural networks with delays. Neurocomputing 68 (2005) 196-207
11. Liu Z., Chen A., Cao J., and Huang L. Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays. Phys. Lett. A 319 (2003) 305-316
12. Liu Z., and Liao L. Existence and global exponential stability of periodic solutions of cellular neural networks with time-vary delays. J. Math. Anal. Appl. 290 (2004) 247-262
13. Kwon O.M., Park J.H., and Lee S.M. On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays. Appl. Math. Comput. 197 (2008) 864-873
14. Park J.H., and Kwon O.M. LMI optimization approach on stability for delayed neural networks of neutral-type. Appl. Math. Comput. 196 (2008) 236-244
15. Xiao B. Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays. Appl. Math. Lett. (2008) 10.1016/j.aml.2008.06.025
16. Xu S., Lam J., Ho D.W.C., and Zou Y. Delay-dependent exponential stability for a class of neural networks with time delays. J. Comput. Appl. Math. 183 (2005) 16-28
17. Liu B. Almost periodic solutions for Hopfield neural networks with continuously distributed delays. Math. Comput. Simulation 73 (2007) 327-335
18. Fink A.M. Almost Periodic Differential Equations. Lecture Notes in Mathematics vol. 377 (1974), Springer, Berlin
19. He C.Y. Almost Periodic Differential Equation (1992), Higher Education Publishing House, Beijing (in Chinese)