The delay logistic map with two types of q-deformations: Tsallis andQuantum-group type are studied. The stability of the map and its bifurcationscheme is analyzed as a function of the deformation and delay feedbackparameters. Chaos is suppressed in a certain region of deformation and feedbackparameter space. The steady state obtained by delay feedback is maintained inone type of deformation while chaotic behavior is recovered in another typewith increasing delay.
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