Qualitative analysis of a ratio-dependent Chemostat model with production of toxin. (Chinese. English summary) Zbl 1399.34140
Summary: A ratio-dependent chemostat model with production of toxin is investigated. A detailed qualitative analysis about existence of its solutions and the local asymptotic stability of its equilibria is carried out. Using the Lyapunov-LaSalle invariant principle, we obtain sufficient conditions for the global asymptotic stability of the equilibria. Our results demonstrate that under different conditions, not only the principle of competitive exclusion but also the coexistence of competition is established.
MSC:
34C60 | Qualitative investigation and simulation of ordinary differential equation models |
92D25 | Population dynamics (general) |
34D23 | Global stability of solutions to ordinary differential equations |
34D05 | Asymptotic properties of solutions to ordinary differential equations |