Noise and autowave processes

Abstract

The fundamental kinetic equations (1.1) for AW processes are obtained by statistical averaging. Indeed, the “concentrations” or “velocities” of the kinetic variables are certain averaged values. In principle an arbitrary deterministic model corresponds to a stochastic model whose kinetic interactions are described by the probabilities of elementary events that occur in small time intervals in small elementary volumes. Noise arising in discrete interactions will become small after averaging if the number of interacting objects (molecules, living organisms) is large. We refer to such types of noise as “natural noise” in the following. However they can also be important in systems with a small number of interacting objects, some examples are ecological communities, systems of genes and organelles in a living cell. Even small amounts of noise can have a substantial effect in systems with concentrations near bifurcation points. Natural noise also has a pronounced effect on multistationary systems. It is interesting to note that in relaxation-type auto-oscillatory chemical reactions there may be time intervals during which the concentration of reactants decreases by many orders of magnitude. The part played by natural fluctuations increases sharply (Zhabotinskii 1974; Romanovskii et al. 1975).