| Title:
|
Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations (English) |
| Author:
|
Stamov, Gani Tr. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
67-76 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a result on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations. The result is obtained by means of piecewise continuous Lyapunov functions and a comparison principle. (English) |
| Keyword:
|
moving invariant set |
| Keyword:
|
stability theory |
| Keyword:
|
uncertain impulsive differential-difference system |
| MSC:
|
34A37 |
| MSC:
|
34K45 |
| idZBL:
|
Zbl 1212.34225 |
| idMR:
|
MR2504689 |
| DOI:
|
10.21136/MB.2009.140641 |
| . |
| Date available:
|
2010-07-20T17:48:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140641 |
| . |
| Reference:
|
[1] Bainov, D., Kostadinov, S., Nguyen, Van Min: Dichotomies and Integral Manifolds of Impulsive Differential Equations.SCT Publishing, Singapore (1994). |
| Reference:
|
[2] Bainov, D., Stamova, I. M.: Vector Lyapunov functions and conditional stability for systems of impulsive differential-difference equations.ANZIAM J. 42 (2001), 341-353. Zbl 0980.93074, MR 1818254, 10.1017/S1446181100011986 |
| Reference:
|
[3] Bainov, D., Dishliev, A. B., Stamova, I. M.: Continuous dependence of solutions of impulsive systems of differential-diference equations on initial data and on parameter.Bol. Soc. Parana. Mat. 18 (1998), 21-34. MR 1769790 |
| Reference:
|
[4] Lakshmikantham, V., Leela, S., Martynyuk, A. A.: Stability Analysis of Nonlinear Systems.Marcel Dekker, New York (1989). Zbl 0676.34003, MR 0984861 |
| Reference:
|
[5] Lakshmikantham, V., Leela, S., Martynyuk, A. A.: Practical Stability of Nonlinear Systems.World Scientific Publishing, Singapore (1990). Zbl 0753.34037, MR 1089428 |
| Reference:
|
[6] Lakshmikantham, V., Vatsala, S. A.: Stability of moving invariant sets.Advances in Nonlinear Dynamics. Langhorne, PA: Cordon and Breach. Stab. Control Theory Methods Appl. {\it 5} (1997), 79-83 Sivasundaram, S. Zbl 0947.34039, MR 1479421 |
| Reference:
|
[7] Shendge, G. R.: A new approach to the stability theory of functional differential equations.J. Math. Anal. Appl. 95 (1983), 319-334. MR 0716086, 10.1016/0022-247X(83)90110-5 |
| Reference:
|
[8] Siljak, D. D., Ikeda, M., Ohta, Y.: Parametic stability.Proccedings Universita di Genova-Ohio State University Joint Conference: Birkhauser (1991), 1-20. MR 1125087 |
| Reference:
|
[9] Stamov, G.: Stability of moving invariant maniolds for impulsive differential equations.J. Tech. Univ. Plovdiv Fundam. Sci. Appl., Ser. A Pure Appl. Math. 7 (1999), 99-107. MR 1834207 |
| Reference:
|
[10] Stamov, G.: Stability of moving conditionally manifolds for impulsive differential equations.Adv. Stud. Contemp. Math. (Kyungshang) 9 (2004), 99-107. MR 2067833 |
| Reference:
|
[11] Stamov, G.: Impulsive integro-differential equations and stability of moving invariant maniolds.Methods Appl. Anal. 14 (2007), 69-76. MR 2392627 |
| Reference:
|
[12] Stamova, I., Stamov, G.: Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics.J. Comput. Appl. Math. 130 (2001), 163-171. Zbl 1022.34070, MR 1827978, 10.1016/S0377-0427(99)00385-4 |
| Reference:
|
[13] Vatsala, A. S., Deo, G. S.: Stability of moving invariant sets for functional differential systems.Int. J. Nonlin. Diff. Eq.: Theory, Methods and Appl. 3 (1997), 179-186. |
| . |
