March  2007, 7(2): 351-363. doi: 10.3934/dcdsb.2007.7.351

A model function for non-autonomous bifurcations of maps

1. 

Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

Received  February 2006 Revised  October 2006 Published  December 2006

In this paper, we introduce a class of one-dimensional non-autonomous dynamical systems that allow an explicit study of their orbits, of the associated variational equations as well as of certain types of bifurcations. In a special case, the model class can be transformed into the non-autonomous Beverton-Holt equation. We use these model functions for analyzing various notions of non-autonomous transcritical and pitchfork bifurcations that have been recently proposed in the literature.
Citation: Thorsten Hüls. A model function for non-autonomous bifurcations of maps. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 351-363. doi: 10.3934/dcdsb.2007.7.351
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