Next: Scaling properties in
Up: Publicat_index
Previous: Unfolding Dimension and
R.M. Dünki, PHYSICA D, 100: 301 - 310, (1997)
Keywords
Intermittency, Power Law, 1/f behaviour, Laminar Sequence, Meta-map, Invariants.
Intermittent behaviour has been found in many systems able to switch between
two different dynamic states e.g between long laminar phases and short chaotic
bursts. Despite the apparently high dimensional complexity, certain 1
dimensional maps are known to mimic properties of such dynamics. To these
belongs the iterative map + )
1, giving rise to long laminar lengths.
The statistics of the laminar lengths are of special interest.
Starting from this map, we
are interested in the values of which arise after passing
through the modulo operation. These determine the laminar lengths uniquely.
A 1-D meta-map =
f( ) is derived heuristically.
It is used to
calculate statistical properties of the laminar phases. Our results show
an improvement for the behaviour of short and very long laminar phases as
compared to
earlier analytical results. Introducing the concept of the generic starting
value, we find laminar phases not to be strictly independent of
their predecessors.
Ruedi Duenki
Mon Dec 23 10:41:26 MET 1997