Determining Lyapunov exponents from a time series
نویسندگان
چکیده
منابع مشابه
Computations of the Lyapunov exponents from time series
In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefo...
متن کاملDetermination of the Largest Lyapunov Exponents Based on Time Series
Submitted: Sep 8, 2013; Accepted: Nov 7, 2013; Published: Nov 12, 2013 Abstract: The evaluation problem of transient processes was considered from the viewpoint of their exponential convergence, as a criterion of system stability. To evaluate the exponential convergence, Lyapunov exponents are used. There was developed a number of procedures to evaluate the first Lyapunov exponent based on time...
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Nonlinear dynamical systems often exhibit chaos, which is characterized by sensitive dependence on initial values or more precisely by a positive Lyapunov exponent. Recognizing and quantifying chaos in time series represents an important step toward understanding the nature of random behavior and revealing the extent to which short-term forecasts may be improved. We will focus on the statistica...
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The new method presented in this study was directly based on the consideration that ophthalmic arterial Doppler signals are chaotic signals. This consideration was tested successfully using the nonlinear dynamics tools, like the computation of Lyapunov exponents. Multilayer perceptron neural network (MLPNN) architecture was formulated and used as a basis for determining variabilities such as st...
متن کاملCharacteristic distributions of finite-time Lyapunov exponents.
We study the probability densities of finite-time or local Lyapunov exponents in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are significant finite-size corrections, which are coordinate dependent. Depending on the nature of the dynamical state, the distribution of local Lyapunov exponents has...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 1985
ISSN: 0167-2789
DOI: 10.1016/0167-2789(85)90011-9