American Institute of Mathematical Sciences

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March  2007, 7(2): 201-218. doi: 10.3934/dcdsb.2007.7.201

Nonlinear age structured model with cannibalism

Fadia Bekkal-Brikci 1, , Khalid Boushaba 2, and  Ovide Arino 3,

1. 

Institut de Recherche pour le Développement, 32 avenue Henri Varagnat 93143 Bondy Cedex, France
2. 

Iowa State University, Department of Mathematics, 482 Carver Hall Ames, IA 50011
3. 

UR Geodes. IRD, Centre de Bondy, 32, Av. Henri Varagnat, 93143 Bondy cedex

Received  January 2006 Revised  November 2006 Published  December 2006

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.
Keywords: existence, nonlinear age-structured population model, uniqueness and asymptotic stability., cannibalism.
Mathematics Subject Classification: Primary: 34Gxx, 92D25; 37K2.
Citation: Fadia Bekkal-Brikci, Khalid Boushaba, Ovide Arino. Nonlinear age structured model with cannibalism. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 201-218. doi: 10.3934/dcdsb.2007.7.201
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