MOVING TOWARD AN UNSTABLE EQUILIBRIUM - SADDLE NODES IN POPULATION SYSTEMS

1. We identify an unstable equilibrium with a two-dimensional stable m anifold and a one-dimensional unstable manifold in a three-state varia ble (larva, pupa, adult) insect population growth model. 2. The saddle node forecasts that the time series of some initial numbers of larvae , pupae and adults are drawn closely to the unstable equilibrium befor e approaching the asymptotic stable attractor (a two-cycle), while the time series of other initial points are not. 3. Using two quantitativ e indices, we examine time series from 3 Tribolium experiment for evid ence of the predicted saddle node. We conclude that a saddle node acco unts for the transient dynamics in these data and for the differences between the transient behaviour of different replicates of the same ex periment.