Existence of periodic solutions of a continuous flow bioreactor model with impulsive control in microorganisms. (English) Zbl 1361.34050
Summary: In this paper, we aim to investigate the dynamics and existence of periodic solutions of a state-dependent impulsive model for continuous flow bioreactors. In this model, the Monod’s growth rate is employed and an impulsive control strategy is used to control the quantity of microorganisms. Our study shows all solutions of the model are bounded; and the order-1 periodic solution exists under certain conditions. At the end of this paper, numerical simulations have been carried out to demonstrate our theoretical results and the performance of the bioreactor.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 92D25 | Population dynamics (general) |
| 34A34 | Nonlinear ordinary differential equations and systems |
Keywords:
order-1 periodic solution; order-2 periodic solution; stability; impulsive model; bioreactorReferences:
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