Stability index of linear random dynamical systems
Visualitza/Obre
Cita com:
hdl:2117/344087
Tipus de documentArticle
Data publicació2021
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement 4.0 Internacional
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.
CitacióCima, A.; Gasull, A.; Mañosa, V. Stability index of linear random dynamical systems. "Electronic journal of qualitative theory of differential equations", 2021, núm. 15, p. 1-27.
ISSN1417-3875
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
Stability index.pdf | 559,7Kb | Visualitza/Obre |