Part-metric and its applications in discrete systems

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摘要

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.

论文关键词:Part-metric,Global asymptotic stability,Difference equation,Cyclic discrete dynamic system

论文评审过程:Available online 20 December 2013.

论文官网地址:https://doi.org/10.1016/j.amc.2013.11.073