A System of Resource-Based Growth Models with Two Resources in the Unstirred Chemostat

Models of single-species growth in the unstirred chemostat on two growth-limiting, nonreproducing resources are considered. For the case of two complementary resources, the existence and uniqueness of a positive steady-state solution is established. It is also proved that the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values. For the case of two substitutable resources, the existence of a positive steady-state solution is determined for a range of the parameter (m, n). Techniques include the maximum principle, monotone method and global bifurcation theory. The longtime behavior of the corresponding limiting system is given for a range of (m, n). In the special case of m=n, the uniqueness and global attractivity of the positive steady-state solution of the original system is established.