In the present work we present numerical results which support further a 2
" -type bifurcation scenario for the interior of the Fatou sets, as suggest
ed by the smooth decomposition method introduced by Peinke, Parisi, Rohrich
t and Rossler [Z. Naturforsch. 43A (1987) 14-16] when applied to a Mandelbr
ot map subject to noise with a small strength. As the strength of the noise
increases the smooth decomposition methods reveals now a 2 " -type bifurca
tion scenario for the external region of the Fatou sets, at least in the li
mit of our numerical results. (C) 2001 Published by Elsevier Science Ltd.