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Title:	Stability index of linear random dynamical system
Author:	Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions
Abstract:	Preprint
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 p_k, k=0,1,...,n, denote the probabilities that the random variable that assigns to each linear random dynamical system its stability index takes the value k. In this paper we obtain either the exact values p_k, or their estimations by combining the Monte Carlo method with a least square approach that uses some affine relations among the values p_k,k=0,1,...,n. The particular case of n-order homogeneous linear random differential or difference equations is also studied in detail.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics -Differentiable dynamical systems -Stability index -random differential equations -random difference equations -random dynamical systems. -Sistemes dinàmics diferenciables -Classificació AMS::37 Dynamical systems and ergodic theory::37H Random dynamical systems -Classificació AMS::34 Ordinary differential equations::34F05 Equations and systems with randomness -Classificació AMS::39 Difference and functional equations::39A Difference equations -Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Draft Report
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