Lyapunov Exponents of Stochastic Systems and Related Bifurcation Problems

2020 ◽  
pp. 315-327
Author(s):  
Walter V. Wedig
Keyword(s):  
Lyapunov Exponents ◽  
Stochastic Systems ◽  
Bifurcation Problems

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.

Simulation of Moment Lyapunov Exponents for Linear Homogeneous Stochastic Systems

2009 ◽  
Vol 76 (3) ◽  
Author(s):  
Wei-Chau Xie ◽  
Qinghua Huang
Keyword(s):  
Lyapunov Exponents ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Diffusion Processes ◽  
Numerical Algorithms ◽  
Stochastic Dynamical Systems ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Moment Lyapunov Exponents

Moment Lyapunov exponents are important characteristic numbers for describing the dynamic stability of a stochastic system. When the pth moment Lyapunov exponent is negative, the pth moment of the solution of the stochastic system is stable. Monte Carlo simulation approaches complement approximate analytical methods in the determination of moment Lyapunov exponents and provides criteria on assessing the accuracy of approximate analytical results. For stochastic dynamical systems described by Itô stochastic differential equations, the solutions are diffusion processes and their variances may increase with time. Due to the large variances of the solutions and round-off errors, bias errors in the simulation of moment Lyapunov exponents are significant in improper numerical algorithms. An improved algorithm for simulating the moment Lyapunov exponents of linear homogeneous stochastic systems is presented in this paper.

scholarly journals Stability Radii via Lyapunov Exponents for Large Stochastic Systems

2013 ◽  
Vol 6 ◽  
pp. 188-193 ◽  
Author(s):  
Humberto Verdejo ◽  
Luis Vargas ◽  
Wolfgang Kliemann
Keyword(s):  
Lyapunov Exponents ◽  
Stochastic Systems ◽  
Stability Radii
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