Stability index of linear random dynamical systems

Anna Cimà, Armengol Gasull, Víctor Mañosa Fernández

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3 Citas (Scopus)

Resumen

Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution. In particular, for the n dimensional case, the zero solution is globally asymptotically stable if and only if this stability index is n. Fixed n, let X be the random variable that assigns to each linear random dynamical system its stability index, and let pK with k = 0, 1, …, n, denote the probabilities that P(X = k). In this paper we obtain either the exact values pK, or their estimations by combining the Monte Carlo method with a least square approach that uses some affine relations among the values pK, k = 0, 1, …, n. The particular case of n-order homogeneous linear random differential or difference equations is also studied in detail.
Idioma originalInglés
Páginas (desde-hasta)1-27
Número de páginas27
PublicaciónElectronic Journal of Qualitative Theory of Differential Equations
Volumen2021
N.º15
DOI
EstadoAceptada en prensa - 2021

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