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Discrete Dynamics in Nature and Society
Volume 6, Issue 1, Pages 31-35
http://dx.doi.org/10.1155/S1026022601000036

Analytical investigation of the onset of bifurcation cascade in two logistic-like maps

Department of Meteorology and Geophysics, Faculty of Physics, University of Sofia, Bulgaria

Received 6 July 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Two modifications of the classical one-dimensional logistic map are proposed, which permitted analytical study of the onset of the bifurcation (period doubling) cascade. The modified maps are two-parametric ones. This introduces new features in their behaviour and makes them more flexible. The results can prove to be useful in the ecological (population dynamics) modeling, where the logistic map is a basic model and also in other fields of application.