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Volume 10,     Number 1,     Spring 2002

 

GROWTH AND COMPETITION IN THE NUTRIENT DRIVEN SELF-CYCLING FERMENTATION PROCESS
R. J. SMITH AND G. S. K. WOLKOWICZ

Introduction. Self-cycling fermentation is a computer-aided bio- technological process developed for environmental cleanup programs such as sewage treatment or the reduction of toxic waste. Waste (nutrient) in a well-stirred tank is consumed by microorganisms, and used for growth and reproduction. A probe inserted in the tank monitors the system until certain conditions are met. The computer then instigates a rapid emptying and refilling process. A fraction of the contents of the tank is released into the environment and then replaced by an equal volume of fresh medium. The process then begins anew with the microorganism consuming the new medium until the conditions for the emptying and refilling process are met again. Under the right conditions, this cycling continues indefinitely, and the process does not require an operator or any estimate of the natural cycle time of the microorganisms in advance.
Since the duration of the emptying and re lling process is extremely short compared to the cycling time, this can be approximated by an instantaneous change in state. Thus, the system can be modelled by a system of impulsive differential equations. Such systems describe processes that are continuous under most conditions, but undergo instantaneous changes when certain conditions are satisfied. The development of the process is described in Sheppard and Cooper [5] and a model similar to the one discussed here is given in Wincure, Cooper, and Rey [6]. Impulsive differential equations are described in Bainov and Simeonov [1], [2], [3] and Lakshmikantham, Bainov, and Simeonov [4].

 

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