منابع مشابه
Lyapunov spectra with continuous
We present a straightforward and reliable continuous method for computing the full or a partial Lyapunov spectrum associated with a dynamical system specified by a set of differential equations. We do this by introducing a stability parameter β > 0 and augmenting the dynamical system with an orthonormal k-dimensional frame and a Lyapunov vector such that the frame is continuously Gram-Schmidt o...
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We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a Hamiltonian system (a Fermi-Pasta-Ulam chain of oscillators); (ii) a general model for spatiotemporal chaos (the complex Ginzburg-Landau equation); (iii) expe...
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Motivated by the basic problem of studying stability of nonautonomous linear systems, different definitions of spectra have been proposed over the years. We review some of these definitions, paying particular attention to how the spectra may be computed. Since the spectra are given by intervals of the real line, one would like to compute the endpoints of these intervals. As it turns out, these ...
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It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory, we derive numerical and in particular, analytical results that provide insights into the overall behavior of the Lyapunov exponents particularly for strange attractors. The corresponding distri...
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A method using discrete cross-correlation for identifying and removing spurious Lyapunov exponents when embedding experimen tal data in a dimension greater than the origina l system is introduce d. The method uses a distribution of calculated exponent values produced by modeling a single time series many times or multiple instances of a time series. For this task, global models are shown to com...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2013
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/46/25/254013