论文标题
在自动发酵罐中的多个交互式基本资源上的增长：冲动的微分方程方法
Growth on multiple interactive-essential resources in a self-cycling fermentor: An impulsive differential equations approach
论文作者
论文摘要
我们引入了一种在自我循环发酵罐中的单个微生物增长的模型，其中任意数量的资源受到限制，当一个特定底物的浓度达到预定水平时，触发了冲动。该模型是脉冲微分方程系统的形式。如果反应堆无限期地循环而没有人类干预并得出这种情况，我们将其视为成功的操作。在这种情况下，冲动微分方程的系统具有周期性解决方案。我们表明，成功等同于解决方案与该定期解决方案的收敛性。我们提供的条件确保存在周期性解决方案。当它存在时，它是独一无二的。但是，我们还表明，解决方案是否会收敛到该周期性解决方案，因此该模型是否预测反应器成功地运行是初始条件依赖性的。用数值示例说明了分析。
We introduce a model of the growth of a single microorganism in a self-cycling fermentor in which an arbitrary number of resources are limiting, and impulses are triggered when the concentration of one specific substrate reaches a predetermined level. The model is in the form of a system of impulsive differential equations. We consider the operation of the reactor to be successful if it cycles indefinitely without human intervention and derive conditions for this to occur. In this case, the system of impulsive differential equations has a periodic solution. We show that success is equivalent to the convergence of solutions to this periodic solution. We provide conditions that ensure that a periodic solution exists. When it exists, it is unique and attracting. However, we also show that whether a solution converges to this periodic solution, and hence whether the model predicts that the reactor operates successfully, is initial condition dependent. The analysis is illustrated with numerical examples.
