Is the largest Lyapunov exponent preserved in embedded dynamics?
نویسندگان
چکیده
The method of reconstruction for an n-dimensional system from observations is to form vectors of m consecutive observations, which for m > 2n, is generically an embedding. This is Takens’ result. Our analytical examples show that it is possible to obtain spurious Lyapunov exponents that are even larger than the largest Lyapunov exponent of the original system. Therefore, we present examples where the largest Lyapunov exponent may not be preserved under Takens’ embedding theorem. 2000 Elsevier Science B.V. All rights reserved.
منابع مشابه
On chaotic nature of speech signals
Various phonemes are considered in terms of nonlinear dynamics. Phase portraits of the signals in the embedded space, correlation dimension estimate and the largest Lyapunov exponent are analyzed. It is shown that the speech signals have comparatively small dimension and the positive largest Lyapunov exponent
متن کاملAnalysis of chaotic vibration in a hexagonal centrifugal governor system
In this paper, the periodic, quasi periodic and chaotic responses of rotational machines with a hexagonal centrifugal governor are studied. The external disturbance is assumed as a sinusoid effect. By using the forth order Rung-Kutta numerical integration method, bifurcation diagram, largest Lyapunov exponent and Lyapunov dimension are calculated and presented to detect the critical controlling...
متن کاملStudying Transition Behavior of Neutron Point Kinetics Equations Using the Lyapunov Exponent Method
The neutron density is one of the most important dynamical parameters in a reactor. It is directly related to the control and stability of the reactor power. Any change in applied reactivity and some of dynamical parameters in the reactor causes a change in the neutron density. Lyapunov exponent method is a powerful tool for investigating the range of stability and the transient behavior of the...
متن کاملResonant forcing of multidimensional chaotic map dynamics.
We study resonances of chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response. We find that resonant forcing functions complement the separation of nearby trajectories, in that the product of the displacement of nearby trajectories and the resonant forcing is a conserved quantity. As a consequence, the resonant functi...
متن کاملRepresentation of a Physio-psychological Index Through Constellation Graphs
Fingertip pulsations (plethysmograms) were found to obey chaotic dynamics [1]. We applied chaos theory to analysis of the time series of plethysmograms under various human physio-psychological conditions. It found out that the largest Lyapunov exponent of the time series could be used to characterize physio-psychological status. A visual representation method based on constellation graphs was d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000