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Nonlinear Dynamics

A Concise Introduction Interlaced with Code

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  • Easy-to-read up-to-date introductory text to nonlinear dynamics

  • Practical focus, concise text, targeting application-oriented audience

  • All concepts illustrated with executable code snippets using open source software

Part of the book series: Undergraduate Lecture Notes in Physics (ULNP)

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  • ISBN: 978-3-030-91032-7
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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xv
  2. Dynamical Systems

    • George Datseris, Ulrich Parlitz
    Pages 1-19
  3. Non-chaotic Continuous Dynamics

    • George Datseris, Ulrich Parlitz
    Pages 21-36
  4. Defining and Measuring Chaos

    • George Datseris, Ulrich Parlitz
    Pages 37-52
  5. Bifurcations and Routes to Chaos

    • George Datseris, Ulrich Parlitz
    Pages 53-70
  6. Entropy and Fractal Dimension

    • George Datseris, Ulrich Parlitz
    Pages 71-87
  7. Delay Coordinates

    • George Datseris, Ulrich Parlitz
    Pages 89-103
  8. Information Across Timeseries

    • George Datseris, Ulrich Parlitz
    Pages 105-119
  9. Billiards, Conservative Systems and Ergodicity

    • George Datseris, Ulrich Parlitz
    Pages 121-136
  10. Periodically Forced Oscillators and Synchronization

    • George Datseris, Ulrich Parlitz
    Pages 137-155
  11. Dynamics on Networks, Power Grids, and Epidemics

    • George Datseris, Ulrich Parlitz
    Pages 157-173
  12. Pattern Formation and Spatiotemporal Chaos

    • George Datseris, Ulrich Parlitz
    Pages 175-192
  13. Nonlinear Dynamics in Weather and Climate

    • George Datseris, Ulrich Parlitz
    Pages 193-210
  14. Back Matter

    Pages 211-236

About this book

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.

Keywords

  • Nonlinear Dynamics
  • Deterministic Chaos
  • Time Series Analysis
  • Nonlinear Time Series Analysis
  • Practical Introduction
  • Fractal Dimension
  • Lyapunov Exponents
  • Nonlinear Oscillators
  • Synchronization
  • Networks
  • Nonlinear Climate Dynamics
  • Meteorology

Authors and Affiliations

  • Max Planck Institute for Meteorology, Hamburg, Germany

    George Datseris

  • Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

    Ulrich Parlitz

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.

 

Bibliographic Information

Buying options

eBook
USD 39.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-91032-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 49.99
Price excludes VAT (USA)