DYNAMICS OF SIMPLE ONE-DIMENSIONAL MAPS UNDER PERTURBATION

It is known that the one-dimensional discrete maps having single-humpe d nonlinear functions with the same order of maximum belong to a singl e class that shows the universal behaviour of a cascade of period-doub ling bifurcations from stability to chaos with the change of parameter s. This paper concerns studies of the dynamics exhibited by some of th ese simple one-dimensional maps under constant perturbations. We show that the ''universality'' in their dynamics breaks down under constant perturbations with the logistic map showing different dynamics compar ed to the other maps. Thus these maps can be classified into two types with respect to their response to constant perturbations. Unidimensio nal discrete maps are interchangeably used as models for specific proc esses in many disciplines due to the similarity in their dynamics. The se results prove that the differences in their behaviour under perturb ations need to be taken into consideration before using them for model ling any real process.