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Journal of Applied Mathematics
Volume 2017, Article ID 8934295, 14 pages
https://doi.org/10.1155/2017/8934295
Research Article

An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density-Dependent Survival Probabilities

School of Business and Economics, The Arctic University of Norway, Campus Harstad, Havnegata 5, 9480 Harstad, Norway

Correspondence should be addressed to Arild Wikan; on.tiu@nakiw.dlira

Received 12 June 2017; Revised 23 August 2017; Accepted 24 September 2017; Published 17 December 2017

Academic Editor: Urmila Diwekar

Copyright © 2017 Arild Wikan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A discrete age-structured semelparous Leslie matrix model where density dependence is included both in the fecundity and in the survival probabilities is analysed. Depending on strength of density dependence, we show in the precocious semelparous case that the nonstationary dynamics may indeed be rich, ranging from SYC (a dynamical state where the whole population is in one age class only) dynamics to cycles of low period where all age classes are populated. Quasiperiodic and chaotic dynamics have also been identified. Moreover, outside parameter regions where SYC dynamics dominates, we prove that the transfer from stability to instability goes through a supercritical Neimark−Sacker bifurcation, and it is further shown that when the population switches from possessing a precocious to a delayed semelparous life history both stability properties and the possibility of periodic dynamics become weaker.