%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Bekkal Brikci, Fadia
%A Boushaba, K.
%A Arino, Ovide
%T Nonlinear age structured model with cannibalism
%D 2007
%L PAR00001493
%G ENG
%J Discrete and Continuous Dynamical Systems Series B
%@ 1531-3492
%K cannibalism ; nonlinear age structured population model ; existence ; uniqueness and asymptotic stability
%M ISI:000244968400001
%N 2
%P 201-218
%R 10.3934/dcdsb.2007.7.201
%U https://www.documentation.ird.fr/hor/PAR00001493
%V 7
%W Horizon (IRD)
%X In this paper, we analyze theoretically an age structured population model with cannibalism. The model is nonlinear in that cannibalism decreases the birth rate based on total population density. We use degree theory to prove the existence of unique solution. We also investigate the asymptotic stability of the solutions, and prove under special hypotheses, local and global attractivity of a unique nontrivial steady state. We convert the problem to a delay differential equation and prove that quasiconvergence leads to global attraction. Some numerical simulations are presented exhibiting sustained oscillations which may occur when the hypotheses of theoretical analysis are not satisfied.
%$ 020 ; 080