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Volume 3,     Number 2,     Spring 1995

 

OSCILLATIONS CAUSED BY CANNIBALISM
IN A SIZE-STRUCTURED POPULATION MODEL
J.M. CUSHING AND JIA LI

Abstract. A size-structured hierarchical model is derived for the size specific density distribution of a population whose birth, death and growth rates are functions of energy obtained from both cannibalism and alternative food resources. The dynamics of the alternative resources are included in the model. From this integro-partial differential equation model a plane autonomous system is derived for the dynamics of the total population biomass and the alternative resource. When cannibalism is not present it is proved that this system exhibits only global equilibrium dynamics. When cannibalism is included it is shown by examples that sustained oscillations can occur through a Hopf bifurcation to stable limit cycles. This is in contrast to similar models in which the alternative resource is held constant in time.

 

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© 2005, Canadian Applied Mathematics Quarterly (CAMQ)