3 research outputs found
Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements
A generic model of stochastic autocatalytic dynamics with many degrees of
freedom is studied using computer simulations. The time
evolution of the 's combines a random multiplicative dynamics at the individual level with a global coupling through a
constraint which does not allow the 's to fall below a lower cutoff given
by , where is their momentary average and is a
constant. The dynamic variables are found to exhibit a power-law
distribution of the form . The exponent
is quite insensitive to the distribution of the random factor
, but it is non-universal, and increases monotonically as a function
of . The "thermodynamic" limit, N goes to infty and the limit of decoupled
free multiplicative random walks c goes to 0, do not commute:
for any finite while (which is the common range
in empirical systems) for any positive . The time evolution of exhibits intermittent fluctuations parametrized by a (truncated)
L\'evy-stable distribution with the same index . This
non-trivial relation between the distribution of the 's at a given time
and the temporal fluctuations of their average is examined and its relevance to
empirical systems is discussed.Comment: 7 pages, 4 figure