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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 412343, 7 pages
http://dx.doi.org/10.1155/2013/412343
Research Article

An Algebraic Method on the Eigenvalues and Stability of Delayed Reaction-Diffusion Systems

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

Received 2 April 2013; Accepted 8 July 2013

Academic Editor: Xiang Ping Yan

Copyright © 2013 Jian Ma and Baodong Zheng. 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

The eigenvalues and stability of the delayed reaction-diffusion systems are considered using the algebraic methods. Firstly, new algebraic criteria to determine the pure imaginary eigenvalues are derived by applying the matrix pencil and the linear operator methods. Secondly, a practical checkable criteria for the asymptotic stability are introduced.