The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty...

Extreme events are ubiquitous in nature and social society, including natural disasters, accident disasters, crises in public health (such as Ebola and the COVID-19 pandemic), and social security incidents (wars, conflicts, and social unrest). These extreme events will heavily impact financial...

We compute the analytic expression of the probability distributions FAEX,+ and FAEX,− of the normalized positive and negative AEX (Netherlands) index daily returns r(t). Furthermore, we define the α re-scaled AEX daily index positive returns r(t)α and negative returns (−r(t))α, which we...

We investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and the German DAX. The dynamic relaxation both before and after the large fluctuations is characterized by a power law, and the exponents p± usually vary with...

The interactions between investors and investments are of significant importance to understand the dynamics of financial markets. An evolutionary model is proposed to investigate the dynamic behaviors of investors and investments in a market ecology. The investors are divided into two groups,...