Symmetric Jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited
نویسندگان
چکیده
منابع مشابه
Jacobian Free Computation of Lyapunov Exponents
The purpose of this paper is to present new algorithms to approximate Lyapunov exponents of nonlinear differential equations, without using Jacobian matrices. We first derive first order methods for both continuous and discrete QR approaches, and then second order methods. Numerical testing is given, showing considerable savings with respect to existing implementations.
متن کاملLyapunov Exponents of Symmetric Attractors
The Lyapunov exponents of symmetric attractors can be forced to be multiple by “instantaneous symmetries” which fix the attractor pointwise. In this paper, we show that “symmetries on average” which fix the attractor as a set may lead to further multiplicities. This work is motivated by, and provides an explanation for, numerical computations by Aston & Laing of Lyapunov exponents for the compl...
متن کاملLyapunov exponents, dual Lyapunov exponents, and multifractal analysis.
It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of one-dimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps. (c) 1999 American Institute of Physics.
متن کاملLyapunov Exponents
We are interested in iterates of the logistic map T : [0, 1] → [0, 1] defined by
متن کاملLyapunov Exponents
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-...
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: Chaos, Solitons & Fractals
سال: 2012
ISSN: 0960-0779
DOI: 10.1016/j.chaos.2011.12.014