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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 930576, 5 pages
Research Article

The Stability Criteria with Compound Matrices

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 21 February 2013; Accepted 30 May 2013

Academic Editor: Chunrui Zhang

Copyright © 2013 Yazhuo Zhang 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.


The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.