Figure 7.
A schematic illustration of the dynamical mechanisms of the noise-induced collapse and recovery processes. The species abundance is plotted versus the environmental deterioration parameter κ (the bifurcation parameter). The deterministic tipping point corresponds to the birth of a reverse saddle-node bifurcation, while the recovery process in the backward direction is the result of a forward saddle-node bifurcation. When the system is initially in the high abundance state, noise-induced collapse occurs at κc, before the system reaches the reverse saddle-node bifurcation point. When the system is in the low abundance state, noise-induced recovery can occur at κr as κ decreases, before the systems reaches the forward saddle-node bifurcation point.