Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 539087, 23 pages
Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case
1Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech Republic
2Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, 60200 Brno, Czech Republic
3Department of Complex System Modeling, Faculty of Cybernetics, Taras, Shevchenko National University of Kyiv, Vladimirskaya Str., 64, 01033 Kyiv, Ukraine
Received 28 January 2010; Accepted 11 May 2010
Academic Editor: Elena Braverman
Copyright © 2010 Josef Diblík 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.
Many processes are mathematically simulated by systems of discrete equations with quadratic
right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalue of the matrix of linear terms. In addition to the stability investigation, we
also estimate stability domains.