Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Nonlinear age structured model with cannibalism

Pages: 201 - 218, Volume 7, Issue 2, March 2007      doi:10.3934/dcdsb.2007.7.201

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Fadia Bekkal-Brikci - Institut de Recherche pour le Développement, 32 avenue Henri Varagnat 93143 Bondy Cedex, France (email)
Khalid Boushaba - Iowa State University, Department of Mathematics, 482 Carver Hall Ames, IA 50011, United States (email)
Ovide Arino - UR Geodes. IRD, Centre de Bondy, 32, Av. Henri Varagnat, 93143 Bondy cedex, France (email)

Abstract: 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:  cannibalism, nonlinear age-structured population model, existence, uniqueness and asymptotic stability.
Mathematics Subject Classification:  Primary: 34Gxx, 92D25; 37K20.

Received: January 2006;      Revised: November 2006;      Available Online: December 2006.