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Title:
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Stability index of linear random dynamical systems
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Author:
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Cima, A.; Gasull, A.; Mañosa, V.
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Abstract:
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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. © 2021, University of Szeged. All rights reserved. |
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Publication date:
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2021-03-19 |
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Subject (UDC):
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51 - Matemàtiques |
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Subject(s):
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Random difference equations; Random differential equations; Random dynamical systems; Stability index |
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Rights:
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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/ |
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Pages:
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27 p. |
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Document type:
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Article
Article - Published version |
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DOI:
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10.14232/ejqtde.2021.1.15
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Published by:
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University of Szeged
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Publish at:
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Electronic Journal of Qualitative Theory of Differential Equations
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Share:
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