Lyapunov exponents and invariant measures of stochastic systems on manifolds

1986 ◽  
pp. 271-291 ◽  
Author(s):  
Hans Crauel
Keyword(s):  
Lyapunov Exponents ◽  
Invariant Measures ◽  
Stochastic Systems

Monte Carlo Simulation of Moment Lyapunov Exponents

2005 ◽  
Vol 72 (2) ◽  
pp. 269-275 ◽  
Author(s):  
Wei-Chau Xie
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lyapunov Exponents ◽  
Stochastic Systems ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Two Dimensional ◽  
Bounded Noise ◽  
Moment Stability ◽  
Moment Lyapunov Exponents

A Monte Carlo simulation method for determining the pth moment Lyapunov exponents of stochastic systems, which governs the pth moment stability, is developed. Numerical results of two-dimensional systems under bounded noise and real noise excitations are presented to illustrate the approach.

Stochastic Dynamics of a Variable Inertia System via Lyapunov Exponents

2008 ◽  
Author(s):  
S. F. Asokanthan ◽  
X. H. Wang ◽  
W. V. Wedig ◽  
S. T. Ariaratnam
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Stochastic Systems ◽  
Stochastic Dynamics ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Frequency Excitation ◽  
The Stability

Torsional instabilities in a single-degree-of-freedom system having variable inertia are investigated by means of Lyapunov exponents. Linearised analytical model is used for the purpose of stability analysis. Numerical schemes for simulating the top Lyapunov exponent for both deterministic and stochastic systems are established. Instabilities associated with the primary and the secondary sub-harmonic resonances have been identified by studying the sign of the top Lyapunov exponent. Predictions for the deterministic and the stochastic cases are compared. Instability conditions have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. The effects of fluctuation density as well as that of damping on the stability behaviour of the system have been examined. Predicted instability conditions are adequate for the design of a variable-inertia system so that a range of critical speeds of operation may be avoided.

Some properties of invariant measures of non symmetric dissipative stochastic systems

2002 ◽  
Vol 123 (3) ◽  
pp. 355-380 ◽  
Author(s):  
Giuseppe Da Prato ◽  
Arnaud Debussche ◽  
Beniamin Goldys
Keyword(s):  
Invariant Measures ◽  
Stochastic Systems

scholarly journals Estimating invariant measures and Lyapunov exponents

1996 ◽  
Vol 16 (4) ◽  
pp. 735-749 ◽  
Author(s):  
Brian R. Hunt
Keyword(s):  
Invariant Measure ◽  
Lyapunov Exponents ◽  
Invariant Measures ◽  
Continuous Invariant Measure ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Recent Interest ◽  
Absolutely Continuous Invariant Measure ◽  
Time Averages ◽  
Absolutely Continuous Invariant

AbstractThis paper describes a method for obtaining rigorous numerical bounds on time averages for a class of one-dimensional expanding maps. The idea is to directly estimate the absolutely continuous invariant measure for these maps, without computing trajectories. The main theoretical result is a bound on the convergence rate of the Frobenius—Perron operator for such maps. The method is applied to estimate the Lyapunov exponents for a planar map of recent interest.

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