NDLI: Entropy and Lyapunov Exponents Relationships in Stochastic Dynamical Systems

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Jedrzejewski, F.
Copyright Year	2003
Abstract	Stochastic differential equations and classical techniques related to the Fokker-Planck equation are standard bases for the analysis of nonlinear systems perturbed by noise, such as seismic wave propagation in random media and response of structures to turbulent wind. In this paper, a complementary approach based on entropy production is proposed to analyse the stochastic stability of dynamical systems. For a large class of stochastic dynamical systems, it is shown that the entropy information production is equal to the negative sum of Lyapunov exponents as the noise strength tends to zero. This result is correlated to the topological entropy property, which is in some cases such as the hyperbolic case, equal the sum of Lyapunov exponents. Several examples are given to illustrate the proposed procedure.
Sponsorship	Pressure Vessels and Piping Division
Starting Page	101
Ending Page	107
Page Count	7
File Format	PDF
ISBN	0791816958
DOI	10.1115/PVP2003-1822
Volume Number	Problems Involving Thermal Hydraulics, Liquid Sloshing, and Extreme Loads on Structures
Conference Proceedings	ASME 2003 Pressure Vessels and Piping Conference
Language	English
Publisher Date	2003-07-20
Publisher Place	Cleveland, Ohio, USA
Access Restriction	Subscribed
Subject Keyword	Noise (sound) Wind Turbulence Stability Dynamic systems Differential equations Fokker-planck equation Entropy Seismic waves Nonlinear systems
Content Type	Text
Resource Type	Article

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