Exponential stability of nonlinear impulsive neutral differential equations with delays

Nonlinear Analysis, Theory, Methods and Applications

Volumn 67, Issue 5, 2007, Pages 1426-1439

  Xu, Daoyi ^a   Yang, Zhiguo ^a   Yang, Zhichun ^a  

^a SICHUAN UNIVERSITY   (China)

Author keywords

Delay; Exponential stability; Impulse; Neutral; Singular impulsive differential inequality

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; TIME DELAY; TIME VARYING SYSTEMS;

DELAY; NEUTRAL IMPULSE; SINGULAR IMPULSIVE DIFFERENTIAL INEQUALITY;

ASYMPTOTIC STABILITY;

EID: 34247348263     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.07.043     Document Type: Article

References (36)

1. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
2. Nieto J.J. Periodic boundary value problems for first-order impulsive ordinary differential equations. Nonlinear Anal. 51 (2002) 1223-1232
3. Nieto J.J. Basic theory for nonresonance impulsive periodic problems of first order. J. Math. Anal. Appl. 205 (1997) 423-433
4. Nieto J.J. Impulsive resonance periodic problems of first order. Appl. Math. Lett. 15 (2002) 489-493
5. Bainov D.D., and Simenov P.S. Systems with Impulse Effect: Stability Theory and Applications (1989), Ellis Horwood Limited, Chichester
6. Akhmetov M.U., and Zafer A. Stability of the zero solution of impulsive differential equations by the Lyapunov second method. J. Math. Anal. Appl. 248 (2000) 69-82
7. Rogovchenko Y.V. Impulsive evolution systems: Main results and new trends. Dyn. Contin. Discrete Impuls. Syst. 3 (1997) 57-88
8. Qian D., and Li X. Periodic solutions for ordinary differential equations with sublinear impulsive effects. J. Math. Anal. Appl. 303 (2005) 288-303
9. Nieto J.J., and Rodriguez-Lopez R. Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations. J. Math. Anal. Appl. 318 (2006) 593-610
10. J. Li, J.J. Nieto, J. Shen, Impulsive periodic boundary value problems of first-order differential equations, J. Math. Anal. Appl. (in press)
11. Samoilenko A.M., and Perestyuk N.A. Impulsive Differential Equations (1995), World Scientific, Singapore
12. Tang S., and Chen L. Density-dependent birth rate, birth pulses and their population dynamic consequences. J. Math. Biol. 44 (2002) 185-199
13. Zhang X., Shuai Z., and Wang K. Optimal impulsive harvesting policy for single population. Nonlinear Anal. Real World Appl. 4 (2003) 639-651
14. M.U. Akhmet, G.A. Bekmukhambetova, Y. Serinagaoglu, The dynamics of the systemic arterial pressure through impulsive differential equations, Inst. Appl. Math., Middle East Tech. Univ. Ankara, 2005, Turkey, 18 pages. Preprint 34
15. Zhao A., and Nieto J.J. Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems. Math. Comput. Modelling 40 (2004) 509-518
16. Gao S., Chen L., Nieto J.J., and Torres A. Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. VACCINE 24 (2006) 6037-6045
17. Li W., and Huo H. Global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics. J. Comput. Appl. Math. 174 (2005) 227-238
18. Zhang W., and Fan M. Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays. Math. Comput. Modelling 39 (2004) 479-493
19. Franco D., Liz E., Nieto J.J., and Rogovchenko Y.V. A contribution to the study of functional differential equations with impulses. Math. Nachr. 218 (2000) 49-60
20. Xu D., Zhu W., and Long S. Global exponential stability of impulsive integro-differential equation. Nonlinear Anal. 64 (2006) 2805-2816
21. Luo Z., and Shen J. Global existence results for impulsive functional differential equations. J. Math. Anal. Appl. 323 (2006) 644-653
22. Guan Z.H., and Chen G. On delayed impulsive Hopfield neural networks. Neural Netw. 12 (1999) 273-280
23. Liu X., and Ballinger G. Uniform asymptotic stability of impulsive delay differential equations. Comput. Math. Appl. 41 (2001) 903-915
24. Yang Z., and Xu D. Existence and exponential stability of periodic solution for impulsive delay differential equations and applications. Nonlinear Anal. 64 (2006) 130-145
25. Yang Z., and Xu D. Stability analysis of delay neural networks with impulsive effects. IEEE Trans. Circuits Syst.-II: Express Briefs 52 (2005) 517-521
26. Huo H. Existence of positive periodic solutions of a neutral delay Lotka-Volterra system with impulses. Comput. Math. Appl. 48 (2004) 1833-1846
27. Luo Z., and Shen J. Oscillation for solutions of nonlinear neutral differential equations with impulses. Comput. Math. Appl. 42 (2001) 1285-1292
28. Graef J.R., Shen J.H., and Stavroulakis I.P. Oscillation of impulsive neutral delay differential equations. J. Math. Anal. Appl. 268 (2002) 310-333
29. Liu X., and Shen J. Asymptotic behavior of solutions of impulsive neutral differential equations. Appl. Math. Lett. 12 (1999) 51-58
30. Liu X., Shen X., and Zhang Y. A comparison principle and stability for large-scale impulsive delay differential systems. ANZIAM J. 47 (2005) 203-235
31. Kamont Z., Turo J., and Zubik-Kowal B. Differential and difference inequalities generated by mixed problems for hyperbolic functional differential equations with impulses. Appl. Math. Comput. 80 (1996) 127-154
32. Guan Z. Impulsive inequalities and stability of large scale singular measure differential systems with unbounded delays. Dyn. Contin. Discrete Impuls. Syst. 3 (1997) 113-130
33. Xu D., and Yang Z. Impulsive delay differential inequality and stability of neural networks. J. Math. Anal. Appl. 305 (2005) 107-120
34. Horn R.A., and Johnson C.R. Topics in Matrix Analysis vol. 2 (1991), Cambridge University Press, England
35. Xu S., Lam J., Daniel W.C., and Zou Y. Delay-dependent exponential stability for a class of neural networks with time delays. J. Math. Anal. Appl. 183 (2005) 16-28
36. Park J.H. Stability criterion for neutral differential systems with mixed multiple time-varying delay arguments. Math. Comput. Simulation 59 (2002) 401-412