where
and
are the immature and mature parts of the population at time
, respectively,
(density independent) is the fecundity (number of newborns per adult), and
is the fraction (density independent) of the immature population that survives and enters the mature stage one unit time later (
). The parameters
and
may be interpreted as the natural death rates (not the fishing mortality) caused by factors other than cannibalism. The nonlinear interactions in the model are of the Ricker type and the corresponding parameters
will be referred to as the cannibalism parameters. The model has a large parameter region with stable equilibrium points. It may transition from stable to unstable through a (supercritical) Hopf bifurcation, which means that beyond the instability threshold the dynamics are a quasiperiodic orbit restricted to an invariant curve that surrounds the unstable equilibrium
and
).
Browse all topics
