Electron. J. Diff. Eqns., Vol. 2006(2006), No. 106, pp. 1-11.

An age-structured model of cannibalism

Robert Marik, Lenka Pribylova

We investigate the predator-prey model with cannibalism in the predator population, suggested by Magnusson [5] in 1995. We explore the model by a theory of bifurcations, based mainly on the results of Bautin. Among others, we show that the limit cycle appearing in the model due to the Andronov-Hopf bifurcation may be stable or unstable.

Submitted April 3, 2006. Published September 8, 2006.
Math Subject Classifications: 34C23, 37G10.
Key Words: Cannibalism; predator-prey; Hopf bifurcation; Lyapunov coefficient.

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Robert Marik
Dept. of Mathematics, Mendel University
Zemedelska 3, 613 00 Brno, Czech Republic
email: marik@mendelu.cz
Lenka Pribylova
Dept. of Applied Mathematics, Masaryk University
Janackovo nam. 2a, 662 95 Brno, Czech Republic
email: pribylova@math.muni.cz

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