The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via
several different numerical techniques. In this review paper, we present a self-contained and …

Understanding the role of meteorology in determining air pollutant concentrations is an
important goal for better comprehension of air pollution dispersion and fate. It requires …

In the present data-rich era, we know that time series of many variables can hardly be
interpreted as regular movements plus some stochastic noise. For half a century, we have …

Reconstructing state-space dynamics from scalar data using time-delay embedding requires
choosing values for the delay τ and the dimension m. Both parameters are critical to the …

Scaling regions—intervals on a graph where the dependent variable depends linearly on
the independent variable—abound in dynamical systems, notably in calculations of …

A method is presented to estimate KS entropy from time series of a high-dimensional
complex system. We focus on partitioned entropy, which measures the complexity of data …

Motivation The circadian rhythm drives the oscillatory expression of thousands of genes
across all tissues. The recent revolution in high-throughput transcriptomics, coupled with the …

Permutation entropy is a powerful tool for quantifying the complexity of a signal which
includes measuring the regularity of a time series. Additionally, outside of entropy and …

Die dominanten mathematischen Regeln eines dynamischen Systems aus Daten zu
ermitteln ist weiterhin eine Herausforderung, welche besonders schwierig wird, wenn die …

In this book, we compared different neural approaches in the forecasting of chaotic
dynamics, which are well-known for their complex behaviors and the difficulty of their …