Dynamics, Complexity and Time Series Analysis

TL;DR

This paper offers an accessible, comprehensive introduction to dynamical systems, covering fundamental concepts, recent research, and practical exercises suitable for readers with basic undergraduate mathematics background.

Contribution

It provides a linguistically accessible yet thorough overview of dynamical systems and their applications, including recent research topics and exercises for learners.

Findings

Includes recent research topics in dynamical systems

Provides practical exercises for understanding concepts

Covers applications of time series analysis in dynamical systems

Abstract

The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not essential and readers are only assumed to have familiarity with foundational undergraduate mathematics topics of calculus, linear algebra and rudimentary statistics. A variety of extended topics on recent publications and research activities in the field have been included in the last four chapters, which the interested reader may use as an introduction into further reading. A collection of exercises and questions both theoretical and computational are also included in this text.