Stability index of linear random dynamical systems

Cima Anna and Gasull Armengol and Mañosa Víctor: Stability index of linear random dynamical systems. (2021)

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Abstract

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.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2021
Number: 15
ISSN: 1417-3875
Number of Pages: 27
Dimensions: 10.14232/ejqtde.2021.1.15
Language: English
Uncontrolled Keywords: Differenciálegyenlet
Additional Information: Bibliogr.: p. 25-27. ; összefoglalás angol nyelven
Date Deposited: 2021. Nov. 08. 10:11
Last Modified: 2021. Nov. 08. 10:11
URI: http://acta.bibl.u-szeged.hu/id/eprint/73667

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