Numerical bifurcation analysis of a nonlinear stage structured cannibalism population model

摘要

We study the long-term dynamics of a two-dimensional stage structured population model for the Barents Sea cod stock with nonlinear cannibalism terms introduced by Wikan and Eide (2004). The model is represented by a two-dimensional system of difference equations for two stages of population. Following Wikan and Eide, we consider three special cases of the original model with different ranges of cannibalism pressures on the newborn, immature and the oldest part of immature. Using the map version of the software CL_MATCONT, we discuss mathematical features of the model that were not considered heretofore. This includes the continuation of curves of codimension 1 bifurcations of fixed points and normal form analysis of codim 1 and codim 2 bifurcations. In this way, we can compute the stability domains of the map and its iterates. We concentrate in particular on the third and fourth iterates of the map and their relation to the 1:3 and 1:4 resonant Neimark-Sacker (NS) points.