The Chemostat with Periodic Washout Rate

The focus in this chapter will be on the possibility of coexistence of two competitors competing for a single nutrient in a chemostat with an oscillatory washout rate. Therefore, an exhaustive study of sufficient conditions for competitive exclusion to hold, as was carried out in Chapter 1, will not be made here. The reference [BHW2J may be consulted for results of this type. 

The main change in this system compared to (5.1) of Chapter 1 is that the constant washout rate D of (5.1) is replaced by a positive, continuous, periodic function (/)  

In other words, the functional response / is monotone increasing. Note that it need not be bounded. 

In dealing with periodic functions the following notation is convenient. If g is a continuous w-periodic function then g will denote the mean value of g  

The system displayed previously will be scaled by measuring 5 in units of and Xj in units of 7,S°. If time is measured in units of D , the system takes the form  

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When (3.3) holds for the /th competitor, that competitor can survive in the chemostat in the absence of competition and with its concentration oscillating in response to the periodically varying washout rate. This is the content of the next result. 

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