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## Two-dimensional Plots

What does it do? The most common display type that you will use is a 2-d plot. Such displays may be used to plot one coordinate of a differential equation against the independent variable, or to plot one dependent variable against another. They can also be used to plot a user-defined function against a variable. On the other hand, if all you want to do is to plot a function, there are many other better tools available, such as Maple, Mathcad, Matlab, or Mathematica. DynaSys is designed explicitly for plotting solutions to dynamical systems.

How do I use it? After your 2-d display is created, you may want to set the variables to be plotted and their ranges through the display dialog box. You may control most aspects of the appearance of the display through that. However, there are several other tools available to facilitate drawing in the 2-d plot.

• To draw an orbit in the window from the current initial conditions, simply click the button on the toolbar that is marked with a small red arrow. As an alternative, you might select the 'Compute Orbit' item from the Orbits menu.
• To set an initial condition to the coordinates of a point in the display, click the point using the right mouse button. As an alternative, you may click the button on the toolbar labeled IC.
• To set the initial condition and then draw the orbit through that point, double-click the point on the screen where the condition is to be set.
• If there are more variables in the current set of equations than appear in the display, then all variables not shown in the display retain their existing initial conditions.
• You may set the direction in which you want to see solutions, e.g. forward in time, backward, or both.

What are the defaults? The default display contains the rectangle (-10,10)x(-10,10). The display has a bounding box, shows axes labeled with tick marks by default, and shows trajectories and nullclines, if any. It does not show direction fields initially. By default, the program tracks solutions for ten units of time both forward and backward, i.e. values for the independent variable from -10 to 10.

This type of display appears by default when you type a set of equations involving one or two differential equations. In the first case, the independent variable appears on the horizontal axis, while the dependent variable appears on the vertical axis. In the latter case, the display is set to show a phase portrait, with both dependent variables on the axes.

Next: Example Up: Displays Previous: Changing Displays

Kevin Cooper
Wed Sep 30 15:21:52 PDT 1998