In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscop...In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ＂microorganism-extinction＂ periodic solution. Further, we establish the sufficient conditions for the global attractivity of the microorganism-extinction periodic solution. Using new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delay is ＂profitless＂.展开更多
基金The National Natural Science Foundation of P.R.China[11201399]The Scientific Research Programmes of Colleges in Xinjiang[XJEDU2012S20]+1 种基金Cultivation Project Young Scientific Innovative Talents(2013731017)Academic Discipline Project of Xinjiang Medical University Health Measurements and Health Economics(XYDXK50780308)
基金Project supported by the National Natural Science Foundation of China(Nos.10471117 and 10771179)the Natural Science Foundation of Shandong University of Science and Technology(No.05g016)
文摘In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ＂microorganism-extinction＂ periodic solution. Further, we establish the sufficient conditions for the global attractivity of the microorganism-extinction periodic solution. Using new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delay is ＂profitless＂.
基金Supported by The National Natural Science Foundation of P. R. China[10961022,10901130]The Scientific Research Programes of Colleges in Xinjiang [XJEDU2007G01,XJEDU2006I05,XJEDU2008S10]
