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Zbl 1200.39005
Dibl{\'\i}k, Josef; Khusainov, Denys Ya.; Grytsay, Irina V.; Šmarda, Zdenĕk
Stability of nonlinear autonomous quadratic discrete systems in the critical case.
(English)
[J] Discrete Dyn. Nat. Soc. 2010, Article ID 539087, 23 p. (2010). ISSN 1026-0226; ISSN 1607-887X/e

Summary: 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 $\lambda =1$ of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.
MSC 2000:
*39A30
39A12 Discrete version of topics in analysis

Keywords: systems of discrete equations; stability; Lyapunov functions

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