Dynamical analysis of a chemostat model with delayed response in growth and pulse input in polluted environment

被引：0
作者：
Jianjun Jiao
Lansun Chen
机构：
[1] Guizhou Key Laboratory of Economic System Simulation,School of Mathematics and Statistics
[2] Guizhou College of Finance & Economics,Institute of Mathematics
[3] Academy of Mathematics and System Sciences,undefined
来源：
Journal of Mathematical Chemistry | 2009年 / 46卷
关键词：
Chemostat model; Delayed response in growth; Pulse input in polluted environment; Extinction; Permanence;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a chemostat model with delayed response in growth and pulse input in polluted environment is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution. Further, it is globally attractive. The permanent condition of the investigated system is also obtained by the theory on impulsive delay differential equation. Our results reveal that the delayed response in growth plays an important role on the outcome of the chemostat.
引用
收藏
页码：502 / 513
页数：11
相关论文
共 53 条
  • [1] Smith H.(1999)Perturbation of a globally stable steady state Proc. A.M.S. 127 447-453
  • [2] Waltman P.(1994)Competition in the chemostat: global asymptotic behavior of a model with delayed response in growth SIAM J. Appl. Math. 154 456-465
  • [3] Ellermeyer S.F.(1989)Global behavior of an SEIRS epidemic model with delays, the history of the vedalia beetle importation to California and its impact on the development of biological control Ann. Rev. Entomol. 34 1-16
  • [4] Caltagirone L.E.(1994)A remark on the global asymptotic stability of a dynamical system modeling two species competition Hiroshima Math. J. 24 435-445
  • [5] Doutt R.L.(2003)A theoretical and empirical investigation of delayed growth response in the continuous culture of bacteria J. Theor. Biol. 222 485-494
  • [6] Hsu S.B.(1975)The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater J. Theor. Biol. 63 385-395
  • [7] Waltman P.(1981)Application of predator-prey models to disinfection J. Water Pollut. Contr. Fed. 53 378-386
  • [8] Ellermeyer S.F.(1998)Competition in the chemostat when one competitor produces a toxin Jpn. J. Ind. Appl. Math. 15 471-490
  • [9] Ellermeyer S.(1982)Application of surplus production model to access environmental impacts in exploited populations of Daphnia pluex in the laboratory Environ. Pollut. (Ser. A) 28 273-280
  • [10] Hendrix J.(1987)Effects of toxicants on population: a qualitiative approach. IV Resource-consumer-toxicants model, Ecol. Model. 35 249-273
123456