Stability of nonlinear autonomous quadratic discrete systems in the critical case.

*(English)*Zbl 1200.39005Summary: 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.

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\textit{J. Diblík} et al., Discrete Dyn. Nat. Soc. 2010, Article ID 539087, 23 p. (2010; Zbl 1200.39005)

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