On bifurcations, resonances and dynamical behaviour in nonlinear iteroparous Leslie matrix models

Abstract

Leslie matrix models with nonzero nonlinear fecundity elements are under consideration. It is proved that by use of the general Deriso–Schnute recruitment function the supercritical nature of bifurcations in 2- and 3-age class models and a thorough analysis of 1:2 and 1:3 resonance phenomena are also provided. A discussion of impact of coexisting attractors and structures of trapping regions is included as well. Results regarding stabilizing and destabilizing effects as well as dynamical outcomes found in general n-age class models are also presented. Suggestions with respect to where our models may apply are provided too.