Progress in combustion science and engineering has led to the generation of large amounts
of data from large-scale simulations, high-resolution experiments, and sensors. This corpus …

In the last decade, there has been a growing body of literature addressing the utilization of
complex network methods for the characterization of dynamical systems based on time …

The paradigm of deterministic chaos has influenced thinking in many fields of science.
Chaotic systems show rich and surprising mathematical structures. In the applied sciences …

This book introduces readers to the full range of current and background activity in the
rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics …

Currently the training of neural networks relies on data of comparable accuracy but in real
applications only a very small set of high-fidelity data is available while inexpensive lower …

When I encountered the idea of chaotic behavior in deterministic dynami cal systems, it gave
me both great pause and great relief. The origin of the great relief was work I had done …

A practical method is proposed to determine the minimum embedding dimension from a
scalar time series. It has the following advantages:(1) does not contain any subjective …

Synchronization of chaotic systems is frequently taken to mean actual equality of the
variables of the coupled systems as they evolve in time. We explore a generalization of this …

We describe the implementation of methods of nonlinear time series analysis which are
based on the paradigm of deterministic chaos. A variety of algorithms for data …

Understanding the interplay of order and disorder in chaos is a central challenge in modern
quantitative science. Approximate linear representations of nonlinear dynamics have long …