Stability index of linear random dynamical systems
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. Fixe...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2021
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet |
| Online Access: | http://acta.bibl.u-szeged.hu/73667 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 27 10.14232/ejqtde.2021.1.15 |
| ISSN: | 1417-3875 |