  A route to chaos is studied in 3-dimensional maps of logistic type.
Mechanisms of period doubling for invariant closed curves (ICC) are found for
specific 3-dimensional maps. These bifurcations cannot be observed for ICC in
the 2-dimensional case. When the parameter of the system is modified, localized
oscillations occur on the ICC that give rise to weakly chaotic rings, then to
chaotic attractors, which finally disappear by contact bifurcations. These maps
can be considered as models for the symbiotic interaction of three species.
