In the time evolution of populations, many attractors can be found: fi
xed points, limit cycles and chaotic regimes. Usually, chaotic behavio
ur is observed in species which have well defined breeding seasons and
a high fertility rate. Different mathematical models have been used i
n order to simulate those regimes. In this paper, we use the bitstring
model introduced to simulate the evolution of age-structured populati
ons - the Penna Model - to simulate a sort of cyclic and chaotic behav
iours. In comparison with the standard logistic map, our results show
a time changing lambda parameter.