Abstract
A sequence of mathematical models for a species which engages in cannibalism are investigated. The models treat the species as age-structured, and assume that adults consume the unhatched eggs of their own kind. The McKendrick or von Foerster partial differential equation model is first converted into a set of three coupled, nonlinear ordinary differential equations, and then adjusted to describe cannibalism. Some rather unusual dynamical effects are discovered. These include both a Hopf bifurcation and a catastrophic transition from an asymptotically stable equilibrium point to a stable limit cycle.
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