Abstract
A generic model of stochastic autocatalytic dynamics with many degrees of freedom is studied using computer simulations. The time evolution of the combines a random multiplicative dynamics at the individual level with a global coupling through a constraint which does not allow the 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 nonuniversal, and increases monotonically as a function of c. The “thermodynamic” limit and the limit of decoupled free multiplicative random walks do not commute: for any finite N while (which is the common range in empirical systems) for any positive c. The time evolution of exhibits intermittent fluctuations parametrized by a (truncated) Lévy-stable distribution with the same index This nontrivial relation between the distribution of the at a given time and the temporal fluctuations of their average is examined, and its relevance to empirical systems is discussed.
- Received 28 December 1998
DOI:https://doi.org/10.1103/PhysRevE.60.1299
©1999 American Physical Society