Methods for determination and approximation of domains of attraction in the case of autonomous discrete dynamical systems

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dc.creatorBalint, St.
dc.creatorKaslik, E.
dc.creatorBalint, A. M.
dc.creatorGrigis, A.
dc.date2004-10-06
dc.date2004-10-07
dc.date.accessioned2026-07-07T05:12:57Z
dc.date.available2026-07-07T05:12:57Z
dc.descriptionA method for determination and two methods for approximation of the domain of attraction $D_{a}(0)$ of an asymptotically stable steady state of an autonomous, $\mathbb{R}$-analytical, discrete system is presented. The method of determination is based on the construction of a Lyapunov function $V$, whose domain of analyticity is $D_{a}(0)$. The first method of approximation uses a sequence of Lyapunov functions $V_{p}$, which converges to the Lyapunov function $V$ on $D_{a}(0)$. Each $V_{p}$ defines an estimate $N_{p}$ of $D_{a}(0)$. For any $x\in D_{a}(0)$ there exists an estimate $N_{p^{x}}$ which contains $x$. The second method of approximation uses a ball $B(R)\subset D_{a}(0)$ which generates the sequence of estimates $M_{p}=f^{-p}(B(R))$. For any $x\in D_{a}(0)$ there exists an estimate $M_{p^{x}}$ which contains $x$. The cases $\|\partial_{0}f\|<1$ and $ρ(\partial_{0}f)<1$ are treated separately (even though the second case includes the first one) because significant differences occur.
dc.description17 pages, 6 figures, submitted to "Discrete and Continuous Dynamical Systems" (AIMS)
dc.identifierhttps://arxiv.org/abs/math/0410146
dc.identifierhttp://arxiv.org/abs/math/0410146
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72771
dc.subjectDynamical Systems
dc.subjectOptimization and Control
dc.subject34D20, 39A11
dc.titleMethods for determination and approximation of domains of attraction in the case of autonomous discrete dynamical systems
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