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# Nullclines

This option allows you to draw the nullclines of systems. Nullclines are curves where the right-hand sides vanish. Their intersections show fixed points. They are most useful for two-dimensional models, but XPP lets you draw them for any model. The constraints are the same as in the direction fields option. The menu has 6 items:

- (N)ew draws a new set of nullclines.

- (R)estore restores the most recently computed set.

- (A)uto turns on a flag that makes XPP redraw them every time it is necessary because some other window obscured them.

- (M)anual turns this flag off so that you must restore them manually. The X-axis nullcline is red and the Y-axis nullcline is green.

- (F)reeze allows you to freeze and play back multiple nullclines

  - (F)reeze freezes the current nullclines

  - (D)elete all deletes all frozen nullclines

  - (R)ange lets you vary a parameter through some range, computes the nullclines and stores them

  - (A)nimate redraws all the frozen nullclines erasing the screen between each one. The user specifies a delay between drawing.

- (S)ave saves the nullclines into a file. They can then be plotted using other software.

  NOTE: The way that XPP computes nullclines (by computing zero contours of a two-variable function) means that the nullclines are composed of a series of small line segments. This means that if you try to plot them as a continuous curve, your plotting program will produce garbage. Thus, you should plot them as points and not draw line segments between them. The data file produced has 4 columns. The first two are the x nullcline and the second two are the y nullcline.

  Data is as follows:

      xnx1 xny1 ynx1 yny1
      xnx2 xny2 ynx2 yny2
      ...

  There are an even number of entries.

  The x nullcline consists of segments `(xnx1,xny1),(xnx2,xny2)` between pairs of points. Similarly for the y nullcline.