Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses

Applied Mathematics and Computation

Volumn 216, Issue 2, 2010, Pages 623-630

  Shi, Peilin ^a   Dong, Lingzhen ^a  

^a TAIYUAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Anti periodic solutions; Exponential stability; Hopfield neural networks; Impulses

Indexed keywords

ANTI-PERIODIC SOLUTIONS; EXPONENTIAL STABILITY; PERIODIC IMPULSE; SUFFICIENT CONDITIONS;

EXPONENTIAL FUNCTIONS; NEURAL NETWORKS; PROBLEM SOLVING; STABILITY;

HOPFIELD NEURAL NETWORKS;

EID: 77649236038     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.01.095     Document Type: Article

References (12)

1. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
2. Mohamad S. Exponential stability in Hopfield-type neural networks with impulses. Chaos, Solitons Fract. 32 (2007) 456-467
3. Gopalsamy K. Stability of artificial neural networks with impulses. Appl. Math. Comput. 154 (2004) 783-813
4. Ou C. Anti-periodic solution for high-order Hopfield neural networks. Comput. Math. Appl. 56 (2008) 1838-1844
5. Chen Y., Nieto J.J., and Oregan D. Anti-periodic solutions for fully nonlinear first-order differential equations. Math. Comput. Model. 46 (2007) 1183-1190
6. Van Den Driessche P., and Zou X. Global attractivity in delayed Hopfield neural network models. SIAM J. Appl. Math. 58 (1998) 1878-1890
7. Aizicovici S., Mckibben M., and Reich S. Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities. Nonlinear Anal. 43 (2001) 233-251
8. Cao J. New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys. Lett. A 307 (2003) 136-147
9. Wang L. Stability of Cohen-Grossberg neural networks with distributed delays. Appl. Math. Comput. 160 (2005) 93-110
10. Li Y., Xing W., and Lu L. Existence and global exponential stability of periodic solution of a class neural networks with impulses. Chaos, Solitons Fract. 27 (2006) 437-445
11. Aftabizadeh A.R., Aizicovici S., and Pavel N.H. On a class of second-order anti-periodic boundary value problems. J. Math. Anal. Appl. 171 (1992) 301-320
12. Okochi H. On the existence of periodic solutions to nonlinear abstract parabolic equations. J. Math. Soc. Jpn. 3 40 (1988) 541-553