Qualitative analysis of a producer–scrounger model

In this paper, we consider a producer–scrounger model proposed in [6]. We prove that when the trivial steady state solution or the semi-trivial steady state solution to the system is stable, then the system admits no positive steady state solution, while if both the trial steady state solution and the semi-trivial steady state solution are unstable, then the system admits at least one positive steady state solution. Furthermore, in the one dimension case, we prove that the positive steady state solution, if exists, is unique.