Moment Lyapunov exponents of a two-dimensional system under both harmonic and white noise parametric excitations

2006 ◽  
Vol 289 (1-2) ◽  
pp. 171-191 ◽  
Author(s):  
Wei-Chau Xie
Keyword(s):  
White Noise ◽  
Lyapunov Exponents ◽  
Dimensional System ◽  
Two Dimensional ◽  
Two Dimensional System ◽  
Moment Lyapunov Exponents

Weak Noise Expansion of Moment Lyapunov Exponents of a Two-Dimensional System Under Bounded Noise Excitation

2000 ◽  
Author(s):  
Wei-Chau Xie
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Dimensional System ◽  
Two Dimensional ◽  
Bounded Noise ◽  
Regular Perturbation ◽  
Weak Noise ◽  
Two Dimensional System ◽  
The Moment ◽  
Moment Lyapunov Exponents

Abstract The moment Lyapunov exponents of a two-dimensional system under bounded noise parametric excitation are studied in this paper. The method of regular perturbation is applied to obtain weak noise expansions of the moment Lyapunov exponent, Lyapunov exponent, and stability index in terms of the small fluctuation parameter.

Numerical Determination of Moment Lyapunov Exponents of Two-Dimensional Systems

2005 ◽  
Vol 73 (1) ◽  
pp. 120-127 ◽  
Author(s):  
Wei-Chau Xie ◽  
Ronald M. C. So
Keyword(s):  
Lyapunov Exponents ◽  
Eigenvalue Problems ◽  
Principal Eigenvalue ◽  
Dimensional System ◽  
Two Dimensional ◽  
Bounded Noise ◽  
Partial Differential ◽  
Stochastic Dynamical System ◽  
Moment Lyapunov Exponents

The pth moment Lyapunov exponent of an n-dimensional linear stochastic system is the principal eigenvalue of a second-order partial differential eigenvalue problem, which can be established using the theory of stochastic dynamical system. An analytical-numerical approach for the determination of the pth moment Lyapunov exponents, for all values of p, is presented. The approach is illustrated through a two-dimensional system under bounded noise or real noise parametric excitation. Series expansions of the eigenfunctions using orthogonal functions are employed to transform the partial differential eigenvalue problems to linear algebraic eigenvalue problems, which are then solved numerically. The numerical values obtained are compared with approximate analytical results with weak noise amplitudes.

Effect of partial ordering of a two-dimensional system of scatterers on the anisotropy of its kinetic coefficients

1998 ◽  
Vol 32 (10) ◽  
pp. 1116-1118
Author(s):  
N. S. Averkiev ◽  
A. M. Monakhov ◽  
A. Yu. Shik ◽  
P. M. Koenraad
Keyword(s):  
Partial Ordering ◽  
Dimensional System ◽  
Two Dimensional ◽  
Kinetic Coefficients ◽  
Two Dimensional System
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