Authors: Liu, Wanping
Yang, Xiaofan
Liu, Xinzhi
Stević, Stevo 
Title: Part-metric and its applications in discrete systems
Journal: Applied Mathematics and Computation
Volume: 228
First page: 320
Last page: 328
Issue Date: 1-Feb-2014
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2013.11.073
This paper applies the part-metric method to study some types of higher-order symmetric difference equations with several different exponential parameters. These difference equations are proved to have unique equilibria and some useful inequalities regarding the difference equation functions are formulated. By use of the part-metric and a result given by Kruse and Nesemann (1999) [8], some sufficient conditions on the parameters are given to guarantee the global asymptotic stability of the equilibria. Furthermore, by the part-metric defined on matrices, this approach is also applicable to show the global asymptotic stability of some cyclic discrete dynamic systems. The results of this paper are considered a big improvement over many existing results found in the literature.
Keywords: Cyclic discrete dynamic system | Difference equation | Global asymptotic stability | Part-metric
Publisher: Elsevier
Project: Doctorate Foundation of Educational Ministry of China (Grant No. 20110191110022)
Scholarship Award for Excellent Doctoral Student granted by Ministry of Education (No. 0903005109081-10)

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