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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