Phase Plotter Applet

This applet plots direction fields, (approximate) solution curves, and isoclines for 2 x 2 autonomous systems. You should be able to use this either in the lab or at home, using a web browser that includes Java: make sure that Java is enabled in your "Advanced Preferences". Be patient: the applet takes some time to load, especially if you are calling up using a slow modem.

 Initially you see the "Bounds and Frame" menu. Here you can set the names of the X and Y axis variables and the X and Y axis scales, and then label the axes by clicking "Draw Frame".

  Then change to the "Direction Field" menu (click on "Bounds and Frame" and choose "Direction Field"). Enter the differential equations in the box after "dx/dt" and "dy/dt". Clicking the "Plot field" button will plot the direction field. Enter initial X and Y values in the two boxes after "Initial point [", and click "Solve forward" or "Solve backward" to plot the trajectory with those initial values at t=0: "Solve forward" for t > 0 or "Solve backward" for t < 0.

  Now change to the "Isoclines" menu, and you can plot isoclines. If "Horizontal" or "Vertical" is selected, "Plot isocline" plots the curve along which the trajectories are horizontal or vertical respectively. If "Slope" is selected, it plots the curve along which the slope of the trajectories is the number in the box to the right of "Slope".

  How to Print

  Mathematical Formulas