Existence and global exponential stability of periodic solutions of recurrent cellular neural networks with impulses and delays

Mathematics and Computers in Simulation

Volumn 79, Issue 1, 2008, Pages 14-29

  Gui, Zhanji ^a,b   Yang, Xiao Song ^b   Ge, Weigao ^c  

^a HAINAN NORMAL UNIVERSITY   (China)

^b HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Global exponential stability; Impulsive effect; Neural networks; Periodic solution; Quasi periodic solution; Simulation method

Indexed keywords

ARTIFICIAL INTELLIGENCE; CELLULAR NEURAL NETWORKS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; PERTURBATION TECHNIQUES; RECURRENT NEURAL NETWORKS; SYSTEMS ENGINEERING; TIME VARYING NETWORKS;

CONTINUATION THEOREM OF COINCIDENCE DEGREE THEORY; GLOBAL EXPONENTIAL STABILITY; IMPULSIVE EFFECT; IMPULSIVE PERTURBATIONS; NUMERICAL SIMULATION METHOD; PERIODIC SOLUTION; PERIODIC SOLUTIONS; QUASI-PERIODIC SOLUTION; SIMULATION METHOD;

NEURAL NETWORKS;

EID: 48549089124     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2007.09.001     Document Type: Article

References (21)

1. Akça H., Alassar R., Covachev V., Covacheva Z., and Al-Zahrani E. Continuous-time additive Hopfield-type neural networks with impulses. J. Math. Anal. Appl. 290 (2004) 436-451
2. Bainov D.D., and Simeonov P.S. Stability Theory of Differential Equations with Impulse Effects: Theory and Applications (1989), Ellis Horwood, Chichester
3. Cao J., and Chen T. Globally exponentially robust stability and periodicity of delayed neural networks. Chaos Sol. Fract. 22 4 (2004) 957-963
4. Cao J., and Wang J. Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans. Circ. Syst. I 52 5 (2005) 920-931
5. Chua L.O., and Yang L. Cellular neural networks: Theory. IEEE Trans. Circ. Syst. I 35 (1988) 1257-1272
6. Chua L.O., and Yang L. Cellular neural networks: Applications. IEEE Trans. Circ. Syst. I 35 (1988) 1273-1290
7. Delgado A., Kambhampati C., and Warwick K. Input/output linearization using dynamic recurrent neural networks. Math. Comput. Simul. 41 (1996) 451-460
8. Gaines R.E., and Mawhin J.L. Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag, Berlin
9. Gopalsamy K. Stability of artificial neural networks with impulses. Appl. Math. Comput. 154 (2004) 783-813
10. Guan Z., James L., and Chen G. On impulsive auto-associative neural networks. Neural Networks 13 (2000) 63-69
11. Guan Z., Liu Y., and Wen X. Decentralized stabilization of singular and time-delay large-scale control systems with impulsive solutions. IEEE Trans. Auto. Control. 40 (1995) 1437-1441
12. Gui Z. Biological Dynamic Models and Computer Simulation (2005), Science Press, Beijing
13. Gui Z., and Ge W. Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses. Chaos 16 (2006) 033116, 1-10
14. Gui Z., and Ge W. Existence and uniqueness of periodic solutions of nonautonomous cellular neural networks with impulses. Phys. Lett. A 354 (2006) 84-94
15. Hopfield J.J. Neural networks and physical systems with collective computational abilities. Proc. Natl. Acad. Sci. U. S. A. 79 (1982) 2554-2558
16. Hopfield J.J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. U. S. A. 81 (1984) 3088-3092
17. Lakshmikantham V., Bainovand D.D., and Simeonov P.S. Theory of Impulse Differential Equations (1989), World Scientific, Singapore
18. Li Y. Global exponential stability of BAM neural networks with delays and impulses. Chaos Sol. Fract. 24 (2005) 279-285
19. Lu S., and Ge W. Periodic solutions for a kind of second order differential equation with multiple deviating arguments. Appl. Math. Comput. 146 (2003) 195-209
20. Marcus C.M., and Westervelt R.M. Stability of analog neural networks with delays. Phys. Rev. A 39 (1989) 347-359
21. Sun C., and Feng C. Exponential periodicity and stability of delayed neural networks. Math. Comput. Simul. 66 (2004) 469-478