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AuthorNusse, Helena E. author
TitleDynamics: Numerical Explorations [electronic resource] : Accompanying Computer Program Dynamics / by Helena E. Nusse, James A. Yorke, Eric J. Kostelich
ImprintNew York, NY : Springer US, 1994
Connect tohttp://dx.doi.org/10.1007/978-1-4684-0231-5
Descript XIII, 485 p. online resource

SUMMARY

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


CONTENT

1. Getting the program running -- 1.1 The Dynamics program and hardware -- 1.2 Getting started with Dynamics -- Appendix: Description of the interrupts -- 2. Samples of Dynamics: pictures you can make simply -- 2.1 Introduction -- 2.2 Complex pictures that are simple to make -- Appendix: Command for plotting a graph and Commands from the Main Menu -- 3. Screen utilities -- 3.1 Clear or Refresh screen and set Text Level (Screen Menu SM) -- 3.2 The arrow keys and boxes (BoX Menu BXM) -- 3.3 Initializing trajectories, plotting crosses, drawing circles and their iterates (cross Menu KM) -- 3.4 Drawing axes (AXes Menu AXM) -- 3.5 Windows and rescaling (Window Menu WM) -- 3.6 Setting colors (Color Menu CM and Color Table Menu CTM) -- 4. Utilities -- 4.1 Setting parameters (Parameter Menu PM) -- 4.2 Setting and replacing a vector (Vector Menu VM) -- 4.3 Setting step size (Differential Equation Menu DEM) -- 4.4 Saving pictures and data (Disk Menu DM) -- 4.5 Setting the size of the core (Size of Core Menu SCM) -- 4.6 Printing pictures (PriNter Menu PNM) -- 5. Dimension and Lyapunov exponents -- 5.1 Introduction and the Methods -- 5.2 Lyapunov Menu LM -- 5.3 Examples -- 5.4 Exercises -- 5.5 References related to Dynamics -- 6. Bifurcation diagrams -- 6.1 Introduction and the Methods -- 6.2 BIFurcation diagram Menu BIFM -- 6.3 Examples -- 6.4 Exercises -- 6.5 References related to Dynamics -- 7. Basins of attraction -- 7.1 Introduction and the Methods -- 7.2 Basin of attraction Menu BM -- 7.3 Examples -- 7.4 Exercises -- 7.5 References related to Dynamics -- 8. Straddle trajectories -- 8.1 Introduction and the Methods -- 8.2 Straddle Trajectory Menu STM -- 8.3 Examples -- 8.4 Exercises -- 8.5 References related to Dynamics -- 9. Unstable and stable manifolds -- 9.1 Introduction and the Methods -- 9.2 Unstable and stable manifold Menu UM -- 9.3 Examples -- 9.4 Exercises -- 9.5 References related to Dynamics -- 10. Finding periodic orbits -- 10.1 Introduction and the Methods -- 10.2 Periodic Orbit Menu POM -- 10.3 Examples -- 10.4 Exercises -- 10.5 References related to Dynamics -- 11. Following periodic orbits -- 11.1 Introduction and the Methods -- 11.2 Follow Orbit Menu FOM -- 11.3 Examples -- 11.4 Exercises -- 11.5 References related to Dynamics -- 12. Changing the program -- 12.1 Modifying a process: Recompiling the program -- 12.2 Adding a new map -- 12.3 The vector y and computing Lyapunov exponents -- 12.4 Adding a new differential equation -- 12.5 Getting data printed out or sent to a file -- 13. Dynamics on Unix systems -- 14. Appendix -- 14.1 The map Q -- 14.2 Alphabetical list of the (sub)menus -- 14.3 Tree of the menus -- 14.4 List of menu commands -- 14.5 Tables of the Figures -- 15. References -- 16. Index of the commands and terms


Mathematics Mathematical analysis Analysis (Mathematics) Computer mathematics Physics Mathematics Analysis Mathematical Methods in Physics Numerical and Computational Physics Computational Mathematics and Numerical Analysis



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