The steady-state solution of equation A.1.1, with integer *q* > 2 and disturbance variance set to zero, is a polynomial in *P* with one or three positive real roots. An index of size of the low-*P* attractor, comparable to resilience as defined by Holling (1973), was calculated as follows. At any point in time, given *I*_{t} and *M*_{t}, the roots are calculated. If there are three real roots, the size of the low-*P* attractor is the distance from the low-*P* root to the unstable intermediate root. If there is one real root, it is either on the low-*P* limb of the phase space, or on the high-*P* limb (Fig. 1). If the root is on the high-*P* limb, then the size of the low-*P* attractor is zero. If the root is on the low-*P* limb, then the size of the low-*P* attractor is infinite. In this case, we set the attractor size to a relatively large value (2.0 in Figs. 8-11) so that results could be plotted.