Cima Anna; Gasull Armengol; Mañosa Víctor: Stability index of linear random dynamical systems. (2021)
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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.
| Mű típusa: | Folyóirat |
|---|---|
| Folyóirat/könyv/kiadvány címe: | Electronic journal of qualitative theory of differential equations |
| Dátum: | 2021 |
| Szám: | 15 |
| ISSN: | 1417-3875 |
| Oldalszám: | 27 |
| Méret: | 10.14232/ejqtde.2021.1.15 |
| Nyelv: | angol |
| Kulcsszavak: | Differenciálegyenlet |
| Megjegyzések: | Bibliogr.: p. 25-27. ; összefoglalás angol nyelven |
| Feltöltés dátuma: | 2021. nov. 08. 10:11 |
| Utolsó módosítás: | 2021. nov. 08. 10:11 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/73667 |
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