Statistical properties of dynamical systems with disturbances: Variation in parameters

Citation

Kleczkowski A (1998) Statistical properties of dynamical systems with disturbances: Variation in parameters. Acta Physica Polonica B, 29 (6), pp. 1717-1735. http://www.actaphys.uj.edu.pl/_old/vol29/abs/v29p1717.htm

Abstract
Statistical properties of kinetic equations are studied for reactions in which the (effective) rate decays to zero with time. For such systems the final state depends on initial condition and on the parameters. Time evolution of the probability distribution associated with a concentration of one of the reagents is studied, and analytical formulas are obtained for the case when the parameters are drawn from a random sample, but remain constant for a particular realization. Even if the underlying distribution of the parameters is symmetrical, the resulting distribution of the concentration is highly skewed. This results in a magnification of variability as small differences in the parameters lead to high levels of variability in the outcome of the reaction. The magnification of the variability is also quantified using a concept analogous to the Lyapunov exponent in chaos theory.

Journal
Acta Physica Polonica B: Volume 29, Issue 6