tailieunhanh - Báo cáo hóa học: "Research Article Stability of Linear Dynamic Systems on Time Scales"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Stability of Linear Dynamic Systems on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 670203 12 pages doi 2008 670203 Research Article Stability of Linear Dynamic Systems on Time Scales Sung Kyu Choi 1 Dong Man Im 2 and Namjip Koo1 1 Department of Mathematics Chungnam National University Daejeon 305-764 South Korea 2 Department of Mathematics Education Cheongju University Cheongju 360-764 South Korea Correspondence should be addressed to Namjip Koo njkoo@ Received 31 May 2007 Revised 23 February 2008 Accepted 16 March 2008 Recommended by Martin Bohner We examine the various types of stability for the solutions of linear dynamic systems on time scales and give two examples. Copyright 2008 Sung Kyu Choi et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Continuous and discrete dynamical systems have a number of significant differences mainly due to the topological fact that in one case the time scale T R real numbers and the corresponding trajectories are connected while in other case T Z integers they are not. The correct way of dealing with this duality is to provide separate proofs. All investigations on the two time scales show that much of the analysis is analogous but at the same time usually additional assumptions are needed in the discrete case in order to overcome the topological deficiency of lacking connectedness. Thus we need to establish a theory that allows us to handle systematically both time scales simultaneously. To create the desired theory requires to setup a certain structure of T which is to play the role of the time scale generalizing R and Z. Furthermore an operation on the space of functions from T to the state space has to be defined generalizing the differential and difference operations. This work was initiated by Hilger 1 in the name of