Dynamic consequences of reproductive delay in Leslie matrix models with nonlinear survival probabilities.

The dynamic consequences of reproductive delay in Leslie matrix models with nonlinear survival probabilities p are analyzed. In consideration of two-age classes, proof is presented for a wide range of p functions that, outside the strongly resonant cases, the transfer from stability to instability goes through a supercritical Hopf bifurcation and, moreover, that the nonlinear development has a strong resemblance of three or four cycles, either exact or approximate. In three-age class models, the tendency toward four-periodical dynamics is shown to be even more pronounced, a qualitative finding that gradually disappears as we turn to the higher-dimensional cases. We also prove that for models of any dimension n > 1 theme are regions in parameter space where the equilibrium is unstable at its creation and we demonstrate that the dynamics in this age-class extinguishing case is 2k.n cyclic.