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Dynamics: Numerical Explorations

Accompanying Computer Program Dynamics

  • Book
  • © 1994

Overview

Authors:
  1. Helena E. Nusse

    1. Vakgroep Econometrie, Rijksuniversiteit Groningen, Groningen, The Netherlands
      Institute for Physical Science and Technology, University of Maryland, College Park, USA

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  2. James A. Yorke

    1. Institute for Physical Science and Technology, University of Maryland, College Park, USA

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  3. Eric J. Kostelich

    1. Department of Mathematics, Arizona State University, Tempe, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 101)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Getting the Program Running

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 1-18

  3. Samples of Dynamics: Pictures You Can Make Simply

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 19-124

  4. Screen Utilities

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 125-166

  5. Utilities

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 167-200

  6. Dimension and Lyapunov Exponents

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 201-228

  7. Bifurcation Diagrams

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 229-268

  8. Basins of Attraction

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 269-314

  9. Straddle Trajectories

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 315-346

  10. Unstable and Stable Manifolds

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 347-370

  11. Finding Periodic Orbits

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 371-390

  12. Following Periodic Orbits

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 391-406

  13. Changing the Program

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 407-432

  14. Dynamics on Unix Systems

    • Eric J. Kostelich
    Pages 433-442

  15. Appendix

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 443-458

  16. References

    • Helena E. Nusse, James A. Yorke, Eric J. Kostelich
    Pages 459-466

  17. Back Matter

    Pages 467-485
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Keywords

About this book

Plotting trajectories is a useful capability in exploring a dynamical system, but it is just the beginning. The Maryland Chaos Group developed an array of tools to help visualize the properties of dynamical systems induding automatic method for plotting all "basins and attractors " , and for automatically searching for all computing "straddle trajectories", periodic orbits of a specified period. In the investigations of the Maryland Chaos Group, I. A. Yorke found it useful to be able to combine these various basic tools with each other into so that each new study could benefit a single package that grew with time from the previous programming efforts. He has been writing this software and distributing versions for the last nine years. The resulting program Dynamics requires either a Unix workstation running XII graphics or an IBM PC compatible computer. Eric I. Kostelich has put in a great deal of effort to port the program to Unix workstations. Some basic tools in Dynamics, such as the computation of Lyapunov exponents and the use of Newton's method are standard. The method of computation of stable and unstable manifolds is superior to standard procedures. Dynamics is currently being used extensively in our research and it is being used in undergraduate courses. Dynamics: Numerical Explora#ons provides an introduction to and overview of fundamental tools and numerical methods together with many simple examples. All the numerical methods described in this book are implemented in Dynamics.

Authors and Affiliations

  • Vakgroep Econometrie, Rijksuniversiteit Groningen, Groningen, The Netherlands

    Helena E. Nusse

  • Institute for Physical Science and Technology, University of Maryland, College Park, USA

    Helena E. Nusse, James A. Yorke

  • Department of Mathematics, Arizona State University, Tempe, USA

    Eric J. Kostelich

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