Zhao, Zhong; Song, Xinyu On the study of chemostat model with pulsed input in a polluted environment. (English) Zbl 1187.34063 Discrete Dyn. Nat. Soc. 2007, Article ID 90158, 12 p. (2007). Summary: A chemostat model with pulsed input in a polluted environment is considered. By using the Floquet theorem, we find that the microorganism eradication periodic solution is globally asymptotically stable if the impulsive period \(T\) is more than a critical value. At the same time, we can find that the nutrient and microorganism are permanent if the impulsive period \(T\) is less than the critical value. Cited in 7 Documents MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 34A37 Ordinary differential equations with impulses 34D05 Asymptotic properties of solutions to ordinary differential equations 92D25 Population dynamics (general) 92D40 Ecology PDFBibTeX XMLCite \textit{Z. Zhao} and \textit{X. Song}, Discrete Dyn. Nat. Soc. 2007, Article ID 90158, 12 p. (2007; Zbl 1187.34063) Full Text: DOI EuDML References: [1] J. K. Hale and A. S. Somolinos, “Competition for fluctuating nutrient,” Journal of Mathematical Biology, vol. 18, no. 3, pp. 255-280, 1983. · Zbl 0525.92024 · doi:10.1007/BF00276091 [2] S. B. Hsu, “A competition model for a seasonally fluctuating nutrient,” Journal of Mathematical Biology, vol. 9, no. 2, pp. 115-132, 1980. · Zbl 0431.92027 · doi:10.1007/BF00275917 [3] H. L. Smith, “Competitive coexistence in an oscillating chemostat,” SIAM Journal on Applied Mathematics, vol. 40, no. 3, pp. 498-522, 1981. · Zbl 0467.92018 · doi:10.1137/0140042 [4] G. J. Butler, S. B. Hsu, and P. Waltman, “A mathematical model of the chemostat with periodic washout rate,” SIAM Journal on Applied Mathematics, vol. 45, no. 3, pp. 435-449, 1985. · Zbl 0584.92027 · doi:10.1137/0145025 [5] P. Lenas and S. Pavlou, “Coexistence of three competing microbial populations in a chemostat with periodically varying dilution rate,” Mathematical Biosciences, vol. 129, no. 2, pp. 111-142, 1995. · Zbl 0828.92028 · doi:10.1016/0025-5564(94)00056-6 [6] S. S. Pilyugin and P. Waltman, “Competition in the unstirred chemostat with periodic input and washout,” SIAM Journal on Applied Mathematics, vol. 59, no. 4, pp. 1157-1177, 1999. · Zbl 0991.92035 · doi:10.1137/S0036139997323954 [7] V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Teaneck, NJ, USA, 1989. · Zbl 0719.34002 [8] D. D. Baĭnov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK, 1993. · Zbl 0815.34001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.