Linear phaseplanes I.

Here is how to draw direction fields for linear equations of the form:

x' = ax + b y
y'= cx + dy

  1. Create the following file:
    # a generic planar system 
    param a=-3,b=-1,c=2,d=0
    x'=a*x+b*y
    y'=c*x+d*y
    @ xp=x,yp=y,xlo=-2,xhi=2,ylo=-2,yhi=2
    done
    
    and save it.
  2. Drop it into Winpp.
  3. Click on Phaseplane Grid Parameters and change Dir Fld Grd from 10 to 20
  4. Click on Phaseplane Direct Fld and you will see the field
  5. Look for the little parameter window and change a,b,c,d to whatever and click OK. Click Graphics Redraw (Ctrl R) and it will redraw them!
  6. To draw trajectories, click on Phaseplane Flow