Click on animation to go through the 3 pages. Click again to repeat.

Click through the 3 pages in the above animation a few times to get familiar with the message. On each of the three 3-D graphs the vertical axis is DP / Dt, which ranges from about -35 individuals/generation to +25 individuals/generation. The axis running across the page is N = P/100, running from 0 to 6 (P=0 to 600 pink love spheres). And the other axis, ranging from 13 to 18 is B, the predator efficacy factor.

When DP / Dt > 0 (first page of animation), the population has a tendency to grow. When DP / Dt < 0 (second page of animation), the population has a tendency to shrink.

The boundary between growing and shrinking is shown on page 3 of the animation. This is the curve along which DP / Dt = 0, meaning there's no change in the population. These values of (N,B) are the fixed points.

Notice that the fixed points curve wiggles, and is shown as a green arc on the left, black in the middle, and green again on the right. The green bits are stable (the growth arrows point towards the green bits from both sides), and the black bit is unstable (the growth arrows point away from this bit, meaning that if we get nudged a little off of this bit we will tend to get further off each ensuing generation).

Look at the three pages. Suppose you're at a stable fixed point (N,B). Is it possible to find such a point such that a small change in B will give rise to radical changes in N - that is either a population outbreak, or decimation?