Four-Periodicity in Leslie Matrix Models with Density Dependent Survival Probabilities

Leslie matrix models with a wide range of density dependent survival probability functionspiare studied. It is shown that for allpiwhich lead to nonstationary behavior, the instability is introduced through a supercritical Hopf bifurcation and further, that the dynamics in the unstable parameter regions in most cases has a strong resemblance of 4-cycles, either exact or approximate. Even in the chaotic regime a qualitative character of 4-cycles is preserved.