A system of resource-based growth models with two resources in the unstirred chemostat
This paper is devoted to the two extreme cases in the unstirred chemostat. Let \(S(t)\), \(R(t)\) denote the nutrient concentrations at time \(t\) and \(u(t)\) is the biomass of the population in the culture vessel, then the well-stirred complementary model is given by NEWLINE\[NEWLINE\begin{aligned} S_t & = (S^0-S) D-{1\over y_s} h(S,R)u\\ R_t & =(R^0-R) D-{1\over y_R}h(S,R)u \tag{1}\\ u_t & =[-D+h(S,R)] u\end{aligned}NEWLINE\]NEWLINE where \(S^0>0\) and \(R^0>0\) are constants that represent the input concentrations of the nutrients \(S\) and \(R\), respectively, and \(D\) is the dilution rate, \(y_s\) and \(y_R\) are the corresponding growth yields constants; \(h(S,R)\) is called the response function. The authors establish the existence and uniqueness of a positive steady-state solution for (1). It is also proved that the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values.
scientific article; zbMATH DE number 1642567
scientific article