  In this work we consider a size-structured cannibalism model with the model
ingredients (fertility, growth, and mortality rate) depending on size (ranging
over an infinite domain) and on a general function of the standing population
(environmental feedback). Our focus is on the asymptotic behavior of the
system, in particular on the effect of cannibalism on the long-term dynamics.
To this end, we formally linearize the system about steady state and establish
conditions in terms of the model ingredients which yield uniform exponential
stability of the governing linear semigroup. We also show how the point
spectrum of the linearized semigroup generator can be characterized in the
special case of a separable attack rate and establish a general instability
result. Further spectral analysis allows us to give conditions for asynchronous
exponential growth of the linear semigroup.
