Robert Marik, Lenka Pribylova
Abstract:
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 |
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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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