Time irreversibility is a fundamental property of many time series. We apply the multiscale entropy (MSE) and multiscale time irreversibility (MSTI) to analyze the financial time series, and succeed to classify the financial markets. Interestingly, both methods have nearly the same...

We investigate the impacts of migration on the evolutionary game dynamics in finite populations with community structures in the framework of evolutionary game theory. In contrast to deterministic dynamics, our model incorporates stochastic factors induced by the finite population size. Based on...

In this paper, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA). The method allows us to extend the description of the cross-correlation properties between two time series. MM-DCCA may provide new ways of measuring the nonlinearity of two...

Multiscale entropy (MSE) is an effective method to measure the complexity of signals from complex systems, which has been applied to various fields successfully. However, MSE may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse-graining procedure reduces the...

Multifractal behavior is found in traffic speed time series and mostly measured around the concept of Legendre singularity spectrum. As one of the multifractal spectra, which is the probability distribution of roughness grain exponent, Legendre spectrum is structurally blind to subtle features...

The sharp volatility of West Texas Intermediate (WTI) crude oil price in the past decade triggers us to investigate the price bubbles and their evolving process. Empirical results indicate that the fundamental price of WTI crude oil appears relatively more stable than that of the market-trading...