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Stability of nonlinear autonomous quadratic discrete systems in the critical case. (English) Zbl 1200.39005

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:

39A30 Stability theory for difference equations
39A12 Discrete version of topics in analysis
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