  The delay logistic map with two types of q-deformations: Tsallis and
Quantum-group type are studied. The stability of the map and its bifurcation
scheme is analyzed as a function of the deformation and delay feedback
parameters. Chaos is suppressed in a certain region of deformation and feedback
parameter space. The steady state obtained by delay feedback is maintained in
one type of deformation while chaotic behavior is recovered in another type
with increasing delay.
