Numerical Techniques for Approximating Lyapunov Exponents and Their Implementation
نویسندگان
چکیده
منابع مشابه
Numerical Techniques for Approximating Lyapunov Exponents and Their Implementation
The algorithms behind a toolbox for approximating Lyapunov exponents of nonlinear differential systems by QR methods are described. The basic solvers perform integration of the trajectory and approximation of the Lyapunov exponents simultaneously. That is, they integrate for the trajectory at the same time, and with the same underlying schemes, as integration for the Lyapunov exponents is carri...
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We present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for dynamical systems, as well as of the numerical techniques developed for the computation of the maximal, of few and of all of them. After some historical notes on the first attempts for the numerical evaluation of LCEs, we discuss in detail the multiplicative ergodic theorem of Oseledec [102], which provides th...
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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...
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The analysis of potentially chaotic behavior in biological and biomedical phenomena has attracted great interest in recent years (1–6). Although no universally accepted mathematical definition of the term chaos exists, Strogatz (7) provides a working definition as ‘‘aperiodic long-term behavior in a deterministic system that exhibits sensitive dependence on initial conditions.’’ Aperiodic long-...
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ژورنال
عنوان ژورنال: Journal of Computational and Nonlinear Dynamics
سال: 2010
ISSN: 1555-1415,1555-1423
DOI: 10.1115/1.4002088