Libro de Resúmenes / Book of Abstracts (Español/English)

Resumenes 64
There exist a lot of examples of predator species which feed on some
preferential age class of their prey. On the other hand, when the prey
species is numerous it may develop defense mechanisms and consequently
a lower predation rate is observed. The dynamical consequences of these
two aspects -age structure prey and defense mechanism -are considered in
this chapter. It is analyzed a predator-prey model, where the prey species
has two age classes and it has a size-dependent defense mechanism. The
analysis is based on a model of the form
dx x + y
= x( γ (1 − ) − f( x, y) z−ν),
dt K
dy
= νx−τy−g( y) z,
dt
dz
= z( µ xf( x, y) + βg(
y) −D),
dt
where the term x+y stands for the population of the prey, x is the
reproductive class and y represents the oldest and non-reproductive class.
The defense of the prey based on its size is simulated assuming that
∂f(
x, y)
dg( y)/ y
∂f(
x, y)
< 0, y < 0. Also, we assume that < 0, to introduce a
∂x
dy
∂y
kind of switching effect. So, if the oldest class is large enough, it becomes
the main energy source of predator food.
The pattern of bifurcations of the system is explored when some
parameters change. It is specially interesting the dependence on the
predator biomass conversion rate µ and the predator death rate D of the
dynamical characteristic of the system. A survey of some literature is
included in order to give a glance to the state of the art in this theme.