具有 Beddington-DeAnglis 摄取功能和脉冲状态反馈控制的恒化器模型的周期解。
Periodic solution of a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control.
机构信息
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, PR China.
出版信息
J Theor Biol. 2009 Nov 7;261(1):23-32. doi: 10.1016/j.jtbi.2009.07.016. Epub 2009 Jul 23.
In this paper, a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control is considered. We obtain sufficient conditions of the global asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.
本文考虑了带有 Beddington-DeAnglis 摄取功能和脉冲状态反馈控制的恒化器模型。我们得到了在没有脉冲状态反馈控制的情况下系统全局渐近稳定性的充分条件。我们还得到了脉冲状态反馈控制下的系统具有一阶周期解。给出了一阶周期解存在和稳定性的充分条件。在某些情况下，系统可能存在二阶周期解。我们的结果表明控制措施是有效和可靠的。
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