2026-04-18T02:29:43Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/5312882024-12-20T05:03:42Zcom_2072_199267com_2072_4427col_2072_201036

Stability index of linear random dynamical systems Cima, A. Gasull, A. Mañosa, V. Random difference equations; Random differential equations; Random dynamical systems; Stability index 51 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. © 2021, University of Szeged. All rights reserved. PID2019-104658GB-I00; Generalitat de Catalunya: 2017-SGR-388; Federación Española de Enfermedades Raras, FEDER: 2017-SGR-1617; Agència de Gestió d'Ajuts Universitaris i de Recerca, AGAUR; Ministerio de Ciencia e Innovación, MICINN; Agencia Estatal de Investigación, AEI: DPI2016-77407-P 2021-03-19 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://hdl.handle.net/2072/531288 10.14232/ejqtde.2021.1.15 eng Electronic Journal of Qualitative Theory of Differential Equations L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by-nc-sa/4.0/ info:eu-repo/semantics/openAccess 27 p. application/pdf University of Szeged RECERCAT (Dipòsit de la Recerca de Catalunya)