(Reactions to book review of “Predictions” by Theodore Moetis, in Science, Feb 26, 1993, p. 1349.)

When a “natural growth” S-curve approaches the upper plateau equilibrium, it can do one of three things:

(1) Approach an invariant asymptotically.

(2) Overshoot and start to oscillate, possibly in a damped oscillation if there is a “friction” factor, but possibly undamped. A damped oscillation would be like approaching a single attractor. Note that a sine-wave is another solution to a first-order differential equation, with an exponential (as in (1)) being the other alternative solution. (See my essay The Key.)

(3) Start oscillating after an overshoot as in (2), but then bifurcate repeatedly to give 2, 4, 8…attractors instead of the original one attractor, and finally go chaotic. In this case, it may eventually go to zero even from an initially high value.

Which form will be taken by the human population increase as it hits the ceiling?