Dynamics of simple one-dimensional maps under perturbation |
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Authors: | Somdatta Sinha Parichay K Das |
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Institution: | (1) Centre for Cellular & Molecular Biology, Uppal Road, 500 007 Hyderabad, India;(2) Indian Institute of Chemical Technology, Uppal Road, 500 007 Hyderabad, India |
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Abstract: | It is known that the one-dimensional discrete maps having single-humped nonlinear functions with the same order of maximum
belong to a single class that shows the universal behaviour of a cascade of period-doubling bifurcations from stability to
chaos with the change of parameters. This paper concerns studies of the dynamics exhibited by some of these 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 compared to the other maps. Thus these maps can be classified into two types
with respect to their response to constant perturbations. Unidimensional discrete maps are interchangeably used as models
for specific processes in many disciplines due to the similarity in their dynamics. These results prove that the differences
in their behaviour under perturbations need to be taken into consideration before using them for modelling any real process. |
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Keywords: | Bifurcation chaos ecology one-dimensional map perturbation |
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