We firstly combine multi-scale method (MS) and weighted-permutation entropy (WPE) to analyze chaotic, noisy, and fractal time series, and find that MSWPE can distinguish different nonlinear time series and exhibit a better robustness in the presence of higher levels of noise, a task that...

The residence time around different parts of a chaotic attractor is studied experimentally for nonlinear dynamical system with a double-scroll. It is shown that the dynamics of jumping from one scroll of the attractor to the other produces a distinct low-frequency peak in the otherwise...

We discuss the relation between ensemble and time averages for quasistationary states of low-dimensional symplectic maps that present remarkable analogies with similar states detected in many-body long-range-interacting Hamiltonian systems.

A macroscopic transport equation has been derived from the underlying microscopic dynamics and a general fluctuation-dissipation relation is proposed for a microscopic system composed of the collective degrees of freedom coupled to finite intrinsic ones through a weak interaction. With the aid...

Time complexity is associated with sensitive dependence on initial conditions and severe intrinsic predictability limits, in particular, the ‘butterfly effect’ paradigm: an exponential error growth and a corresponding characteristic predictability time. This was believed to be the universal...

We describe a novel mechanism for inducing traveling-wave attractors in rings of coupled maps. Traveling waves are easily produced when parameters controlling local dynamics vary from site to site. We also present some statistical results regarding the distribution of periodic time-evolutions.

In this paper, we construct low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A...

The stride interval time series in normal human gait is not strictly constant, but fluctuates from step to step in a complex manner. More precisely, it has been shown that the control process for human gait is a fractal random phenomenon, that is, one with a long-term memory. Herein we study the...

We investigate how the adaptation of the competition coefficients of the competing populations for the same limited resource influences the system dynamics in the regions of the parameter space, where chaotic motion of Shilnikov kind exists. We present results for two characteristic values of...

In this work we have applied nonlinear time series analysis to high-frequency currency exchange data. The time series studied are the exchange rates between the US Dollar and 18 other foreign currencies from within and without the Euro zone. Our goal was to determine if their dynamical...