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Local Lyapunov exponents: Sublimiting growth rates of linear random differential equations

By Wolfgang Siegert (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2009
ISBN
3540859632
DOI
10.1007/978-3-540-85964-2
Language
english
Format
PDF
Filesize
2 MB (2039855 bytes)
Series
Lecture Notes in Mathematics 1963
Edition
1
Pages
254\263
Library
Kolxo3
Time added
2009-07-20 03:45:11
Dynamical Systems and Ergodic Theory; Global AnalyEconomicsSocial and Behav. Sciences; Genetics and Populatio

Description

Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.

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