Two one-dimensional dynamical systems discrete in time are presented, where
the variation of one parameter causes a sequence of global bifurcations; a
t each bifurcation the period increases by a constant value (period-increme
nt scenario, usually denoted as a period-adding scenario). We determine all
the bifurcation points and the scaling constants of the period-increment s
cenario analytically. A re-injection mechanism, leading to the period-incre
ment scenario, is discussed. It will be shown, that in systems with more th
an one parameter the scaling constants can depend on the values of the para
meters. (C) 2000 Elsevier Science Ltd. All rights reserved.