- Research Article
- 10.1137/25m1765808
An Extension of the Chemostat Model with Linear Coupling Between Species
- Feb 03, 2026
- SIAM Journal on Applied Dynamical Systems
- Tewfik Sari + 1 more +1
We investigate the classical model of competition of two populations in the chemostat when a linear coupling between the populations is taken into account and the removal rates of the populations are distinct from the dilution rate and their yield coefficients are also distinct. This model extends a model of wall growth and a model of lateral gene transfer, previously studied in the literature. We show the existence and uniqueness of the coexistence equilibrium at which the populations coexist, provided that the input concentration of the chemostat exceeds a critical value, or, equivalently the dilution rate does not exceed a critical value that can be computed explicitly. In contrast with the particular cases of this model, previously studied in the literature, the positive equilibrium can be unstable with the appearance of Hopf bifurcations and sustainable oscillations. We construct the operating diagram of the system, which is the two-parameter bifurcation diagram with respect to the operating parameters, that are the dilution rate of the chemostat and its input nutrient concentration. This study reveals a rich variety of dynamical behaviours, including the emergence and disappearance of stable and unstable limit cycles through Hopf bifurcations and limit point of cycles bifurcations. Furthermore, codimension-two bifurcations such as cusp and generalized Hopf points are identified, highlighting complex transitions in the system's dynamics.
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