We model a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study changes in the existence and the stability of isolated equilibria, as well as changes in the global dynamics, as the nutrient concentration varies. The bifurcations of the system are analytically verified and we identify conditions under which an equilibrium undergoes a Hopf bifurcation and a limit cycle appears. Numerical simulations for specific functional responses illustrate the general results.

中文翻译：

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营养物-猎物-捕食者模型：稳定性和分支

我们使用输入的营养物浓度作为分叉参数，在具有一般功能响应的恒化器中模拟营养物-捕食者-捕食者系统。我们研究随着营养物浓度的变化，孤立平衡的存在和稳定性的变化，以及整体动力学的变化。通过分析验证了系统的分叉，并确定了条件发生平衡的Hopf分叉和出现极限环的条件。特定功能响应的数值模拟说明了一般结果。