Seminar in PSA 106

ABSTRACT:

A population model is considered which discriminates between juvenile
and adult individuals and is formed by a planar system of ordinary
differential equations. The per capita transition rate from the juvenile to the adult
stage is assumed to depend on the respective densities.
If this transition rate is only mildly affected by the juvenile density,
the population either goes extinct or converges to a unique equilibrium.
If there is a strong dependence on the juvenile density, the population
dynamics can become as complex as they can get in the plane. This includes
bistability between several equilibria or between equilibria and periodic
orbits and both super- and sub-critical Hopf bifurcations.
This elementary model gives an idea of the complexity of dynamics one may
expect for more realistic physiologically structured population models.