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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 956359, 13 pages
http://dx.doi.org/10.1155/2012/956359
Research Article

An Algebraic Criterion of Zero Solutions of Some Dynamic Systems

1Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
2Department of Mathematics, Northeast Forestry University, Harbin, Heilongjiang 150040, China

Received 19 October 2012; Revised 7 December 2012; Accepted 7 December 2012

Academic Editor: Allan Peterson

Copyright © 2012 Ying Wang 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.

Abstract

We establish some algebraic results on the zeros of some exponential polynomials and a real coefficient polynomial. Based on the basic theorem, we develop a decomposition technique to investigate the stability of two coupled systems and their discrete versions, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts and the moduli of all roots of a real coefficient polynomial are less than 1.