Nonlinear Dynamics

This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills.

Table of Contents

1 Dynamical Systems

2 Non-chaotic Continuous Dynamics

3 Defining and Measuring Chaos

4 Bifurcations and Routes to Chaos

5 Entropy and Fractal Dimension

6 Delay Coordinates

7 Information Across Timeseries

8 Billiards, Conservative Systems and Ergodicity

9 Periodically Forced Oscillators and Synchronization

10 Dynamics on Networks, Power Grids, and Epidemics

11 Pattern Formation and Spatiotemporal Chaos

12 Nonlinear Dynamics inWeather and Climate

About the Authors

George Datseris is a postdoctoral researcher at the Max Planck Institute for Meteorology, Hamburg (Germany), working on the nonlinear dynamics of climate. He has taught several courses on nonlinear dynamics and has developed interactive applications for use in teaching. He is also the lead developer of the software organization JuliaDynamics, which is by far the largest collection of software on nonlinear dynamics and even includes award winning software like DynamicalSystems.jl.

Ulrich Parlitz works at the Max Planck Institute for Dynamics and Self-Organization, Göttingen (Germany), in the Research Group Biomedical Physics and he is also affiliated with the Faculty of Physics of the University of Göttingen where he teaches for 25 years courses on nonlinear dynamics, data analysis, and complex systems. His main scientific interests include dynamical systems, cardiac dynamics, time series analysis and machine learning.