Comparison of Different Methods for Computing Lyapunov Exponents
نویسندگان
چکیده
منابع مشابه
Analysis of Numerical Methods Suitable for Computing Lyapunov Exponents
Two standard methods for numerically estimating Lyapunov exponents are reviewed and it is noted that a numerical integration scheme that preserves orthonormality is required. A procedure is introduced for modifying arbitrary rth order numerical schemes to preserve orthonormality. Convergence is shown for the particular case when explicit Euler's method is taken as the arbitrary method. This mot...
متن کاملOn the error in computing Lyapunov exponents by QR Methods
We consider the error introduced using QR methods to approximate Lyapunov exponents. We give a backward error statement for linear non-autonomous systems, and further discuss nonlinear autonomous problems. In particular, for linear systems we show that one approximates a “nearby” discontinuous problem where how nearby is measured in terms of local errors and a measure of non-normality. For nonl...
متن کاملComputing Lyapunov Exponents for Time-Delay Systems
The hall mark property of a chaotic attractor, namely sensitive dependence on initial condition, has been associated by the Lyapunov exponents to characterize the degree of exponential divergence/convergence of trajectories arising from nearby initial conditions. At first, we will describe briefly the concept of Lyapunov exponent and the procedure for computing Lyapunov exponents of the flow of...
متن کاملError analysis of a hybrid method for computing Lyapunov exponents
In a previous paper [6] we suggested a numerical method for computing all Lyapunov exponents of a dynamical system by spatial integration with respect to an ergodic measure. The method extended an earlier approach of Aston and Dellnitz [2] for the largest Lyapunov exponent by integrating the diagonal entries from the QR-decomposition of the Jacobian for an iterated map. In this paper we provide...
متن کاملQr-based Methods for Computing Lyapunov Exponents of Stochastic Differential Equations
Lyapunov exponents (LEs) play a central role in the study of stability properties and asymptotic behavior of dynamical systems. However, explicit formulas for them can be derived for very few systems, therefore numerical methods are required. Such is the case of random dynamical systems described by stochastic differential equations (SDEs), for which there have been reported just a few numerica...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1990
ISSN: 0033-068X,1347-4081
DOI: 10.1143/ptp.83.875