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which contains several additonal visualizations.
August 1997
Discussion Paper No. 353
Department of Economics, University of Bielefeld
Abstract
We analyze, mainly numerically, the bifurcation behavior of
the parametrically and externally perturbed logistic map.
Two different approaches toward a bifurcation theory of random
systems are employed; the phenomenological approach which deals with
qualitative changes of stationary measures, and the dynamical
approach which studies the stability of invariant measures
and the occurrence of new invariant measures.
The numerical part of this paper contains a thorough examination of
the perturbed logistic map, where the noise is either a dichotomic
Markov process entering multiplicatively, or a uniformly distributed
i.i.d. process entering additively. We observe interesting
bifurcation scenarios, stabilization by noise, and self-similarity
properties of Lyapunov exponents.
Some analytical results on the existence of stationary and invariant
measures and on their Lyapunov exponents are also given.
Paper
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web page
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