Global stability in a synthrophic chain model (Q1176485)

A mathematical model, originally formulated by \textit{G. E. Powell} [see Theor. Popul. Biol. 30, 17-25 (1986; Zbl 0591.92023)] which describes a synthropic chain of species \(X_ i\), \(1\leq i\leq n\), in a continuous chemostat culture, is considered. Species \(X_ i\) utilizes substrate \(S_ i\) and forms a product \(S_{i+1}\). Substrate \(S_{i+1}\) inhibits the growth of \(X_ i\) and constitutes a growth-limiting substrate of \(X_{i+1}\). For this model, conditions for coexistence of all species are given and the local stability results are extended to global stability.