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 whe...

The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body's standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balanc...

Cellular Automata are simple computational models which can be leveraged to model a wide variety of dynamical systems. Composed of a lattice of discrete cells that take finite number of states based on previous iterations these models differ greatly from dynamic systems that vary continuously in space or time. However given their ability to model many of continuous systems, it could be postulat...

The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional to N−1/5. The time scales determined by these quantities evidently differ from any type of relaxation time found in the previous investigatio...

Dynamical chaos is studied in the Hamiltonian motion of ions confined in a Penning trap and forming so-called microplasmas. The dynamical chaos of the ion motion is characterized by the maximum Lyapunov exponent. Results are reported on the dependence of this exponent on the energy of the system, on the number of ions, as well as on the geometry of the trap. Different dynamical regimes are char...

Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest Lyapunov exponent. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. We present a new method for calculating the largest Lyapunov exponent from an experimental time series. The method ...

Nonlinear phenomena occur in nature in a wide range of apparently different contexts, yet they often display common features, or can be understood using similar concepts. Deterministic chaos and fractal structure in dissipative dynamical systems are among the most important nonlinear paradigms. The spectrum of Lyapunov exponents provides a quantitative measure of the sensitivity to initial cond...

Impulsively synchronized chaos with criterion from conditional Lyapunov exponent is often interrupted by desynchronized bursts. This is because the Lyapunov exponent can not characterize local instability of synchronized attractor. To predict the possibility of the local instability, we introduce a concept of supreme local Lyapunov exponent (SLLE), which is defined as supremum of local Lyapunov...

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

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...