References
- B. Aulbach and S. Hilger, A unified approach to continuous and discrete dynamics, in "Qualitative Theory of Differential Equations"(Szeged, 1988), 37-56, Colloq. Math. Soc. Janos Bolyai, 53, North Holland, Amsterdam, 1990.
- B. Aulbach and S. Hilger, Linear dynamic processes with inhomogeneous time scale, in "Nonlinear Dynamics and Quantum Dynamical Systems"(Gaussig, 1990), 9-20, Math. Res. 59, Akademie-Verlag, Berlin, 1990.
- M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, 2001.
- M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.
- S. K. Choi, Y. H. Goo, and N. J. Koo, Variationally asymptotically stable difference systems, Adv. Difference Equ. 2007 (2007), Article ID 35378, 21 pp.
- S. K. Choi, Y. H. Goo, and N. Koo, h-Stability of dynamic equations on time scales with nonregressivity, Abstr. Appl. Anal. 2008 (2008), Article ID 632473, 13 pp.
-
S. K. Choi and N. J. Koo, Variationally stable difference systems by
$n_{\infty}$ -similarity, J. Math. Anal. Appl. 249 (2000), no. 2, 553-568. https://doi.org/10.1006/jmaa.2000.6910 - S. K. Choi and N. Koo, On the stability of linear dynamic systems on time scales, J. Difference Equ. Appl. 15 (2009), no. 2, 167-183. https://doi.org/10.1080/10236190802008528
- S. K. Choi, N. J. Koo, and S. Dontha, Asymptotic property in variation for nonlinear differential systems, Appl. Math. Lett. 18 (2005), no. 1, 117-126. https://doi.org/10.1016/j.aml.2003.07.019
- S. K. Choi, N. J. Koo, and D. M. Im, Asymptotic equivalence between linear differential systems, Bull. Korean Math. Soc. 42 (2005), no. 4, 691-701. https://doi.org/10.4134/BKMS.2005.42.4.691
- S. K. Choi, N. J. Koo, and K. Lee, Asymptotic equivalence for linear differential systems, Commun. Korean Math. Soc. 26 (2011), no. 1, 37-49. https://doi.org/10.4134/CKMS.2011.26.1.037
-
R. Conti, Sulla
$t_{\infty}$ -similitudine tra matrici e la stabilita dei sistemi differenziali lineari, Atti. Acc. Naz. Lincei, Rend. Cl. Fis. Mat. Nat. 49 (1955), 247-250. - V. Cormani, Liouville's formula on time scales, Dynam. Systems Appl. 12 (2003), no. 1-2, 79-86.
- I. Gohberg, M. A. Kaashoek, and J. Kos, Classification of linear time-varying difference equations under kinematic similarity, Integral Equations Operator Theory 25 (1996), no. 4, 445-480. https://doi.org/10.1007/BF01203027
- S. Hilger, Analysis on measure chains - a unified approach to continous and discrete calculus, Results Math. 18 (1990), no. 1-2, 18-56. https://doi.org/10.1007/BF03323153
- V. Lakshmikantham and S. Leela, Differential and Integral Inequalites with Theory and Applications, Academic Press, New York and London, 1969.
- L. Markus, Continuous matrices and the stability of differential systems, Math. Z. 62 (1955), 310-319. https://doi.org/10.1007/BF01180637
-
W. F. Trench, On
$t_{\infty}$ quasi-similarity of linear systems, Ann. Mat. Pura Appl. 142 (1985), 293-302. https://doi.org/10.1007/BF01766598 - W. F. Trench, Linear asymptotic equilibrium and uniform, exponential, and strict stability of linear difference systems, Comput. Math. Appl. 36 (1998), no. 10-12, 261-267. https://doi.org/10.1016/S0898-1221(98)80027-8