The dynamical models of activated sludge system : stochastic cellular automaton and differential equations
Faculty of Sciences. Biology
International journal of biomathematics
, p. 1-15
University of Antwerp
A stochastic cellular automaton (CA) model for activated sludge system (ASS) is formulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations (ODEs) of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, complexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.