Abstract
The dynamics of set value mapping is considered. For the upper semi-continuous set value maps, the existence of attractors under some conditions and the upper semi-continuity of attractors under the perturbation are proved. Its application in numerical simulation of differential equation is also considered. The upper semi-continuity of attractors in set value maps under the perturbation is used to show the reasonable of subdivision algorithm and interval arithmetic in numerical simulation of differential equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kloeden P E, Lorenz J. Stable attracting sets in dynamical systems and in their one-step discritezations[J]. SIAM J Numer Anal, 1986, 23(5):986–995.
Dellnitz M, Hohmann A. A subdivision algorithm for the computation of unstable manifold and global attractors[J]. Numer Math, 1997, 75(3):293–317.
Caraballo T, Langa J A. On the upper semicontinuity of cocyle attractors for non-autonomous and random dynamical systems[J]. Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 2003, 10(4):491–513.
Caraballo T, Langa J A, Robinson J C. On the upper semicontinuity of attractors for small random perturbations of dynamical systems[J]. Communication in PDEs, 1998, 23(9–10):1557–1581.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (No.10571130)
Rights and permissions
About this article
Cite this article
Li, T. Set value mapping and its application. Appl Math Mech 27, 263–268 (2006). https://doi.org/10.1007/s10483-006-0216-1
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-006-0216-1