Extinction, periodicity and multistability in a Ricker Model of Stage-Structured Populations

Abstract

We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (e.g. adult, juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the non-autonomous case. This gives general conditions for extinction in the biological context. We also study the dynamics of an autonomous special case of the equation that generates multistable periodic and non-periodic orbits in the positive quadrant of the plane.Comment: 26 pages, 2 figures - accepted for publication in the Journal of Difference Equations and Application