Downloads provided by UsageCountsStability index of linear random dynamical systems
Copyright policy ) Anna Cima; Armengol Gasull; Víctor Mañosa;
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 $n.$ Fixed $n,$ let $X$ be the random variable that assigns to each linear random dynamical system its stability index, and let $p_k$ with $k=0,1,\ldots,n,$ denote the probabilities that $P(X=k)$. 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 $p_k,k=0,1,\ldots,n.$ The particular case of $n$-order homogeneous linear random differential or difference equations is also studied in detail.
34 pages, 5 tables
stability index, Classificació AMS::34 Ordinary differential equations::34F05 Equations and systems with randomness, Random dynamical systems, :34 Ordinary differential equations::34F05 Equations and systems with randomness [Classificació AMS], Classificació AMS::39 Difference and functional equations::39A Difference equations, Dynamical Systems (math.DS), random dynamical systems., Random difference equations, random difference equations, 37H10, 34F05, 39A25, 37C75, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], Stability index, QA1-939, random differential equations, FOS: Mathematics, Classificació AMS::37 Dynamical systems and ergodic theory::37H Random dynamical systems, Differentiable dynamical systems, Mathematics - Dynamical Systems, QA Mathematics / matematika, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics, :Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics [Àrees temàtiques de la UPC], :39 Difference and functional equations::39A Difference equations [Classificació AMS], Sistemes dinàmics diferenciables, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, :37 Dynamical systems and ergodic theory::37H Random dynamical systems [Classificació AMS], random dynamical systems, Random differential equations, Mathematics
stability index, Classificació AMS::34 Ordinary differential equations::34F05 Equations and systems with randomness, Random dynamical systems, :34 Ordinary differential equations::34F05 Equations and systems with randomness [Classificació AMS], Classificació AMS::39 Difference and functional equations::39A Difference equations, Dynamical Systems (math.DS), random dynamical systems., Random difference equations, random difference equations, 37H10, 34F05, 39A25, 37C75, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], Stability index, QA1-939, random differential equations, FOS: Mathematics, Classificació AMS::37 Dynamical systems and ergodic theory::37H Random dynamical systems, Differentiable dynamical systems, Mathematics - Dynamical Systems, QA Mathematics / matematika, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics, :Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics [Àrees temàtiques de la UPC], :39 Difference and functional equations::39A Difference equations [Classificació AMS], Sistemes dinàmics diferenciables, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, :37 Dynamical systems and ergodic theory::37H Random dynamical systems [Classificació AMS], random dynamical systems, Random differential equations, Mathematics
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This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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