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 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...

In this work we present a simple mathematical model for a β-type Stirling engine. Despite its simplicity, the model considers all the engine’s relevant thermodynamic and mechanical aspects. The dynamic behavior of the model equation of motion is analyzed in order to obtain the sufficient...

Despite many previous studies on the association between hyperthyroidism and the hyperadrenergic state, controversies still exist. Detrended fluctuation analysis (DFA) is a well recognized method in the nonlinear analysis of heart rate variability (HRV), and it has physiological significance...

Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the...

Ecological systems are complex assemblies of large numbers of individuals, interacting competitively under multifaceted environmental conditions. Recent studies using microbial laboratory communities have revealed some of the self-organization principles underneath the complexity of these...

Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann–Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions, mixing and ergodicity in Gibbs...

We propose a new four state model for disease transmission and illustrate the model with data from the 2003 SARS epidemic in Hong Kong. The critical feature of this model is that the community is modelled as a small-world network of interconnected nodes. Each node is linked to a fixed number of...