Abstract
A chemostat model with periodically pulsed input is considered. By
using the Floquet theorem, we find that the microorganism eradication
periodic solution
A chemostat model with periodically pulsed input is considered. By
using the Floquet theorem, we find that the microorganism eradication
periodic solution
D. D. Baĭnov and D. D. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, 1993.
View at: MathSciNetG. Ballinger and X. Liu, “Permanence of population growth models with impulsive effects,” Mathematical and Computer Modelling, vol. 26, no. 12, pp. 59–72, 1997.
View at: Publisher Site | Google Scholar | MathSciNetG. 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.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. D'Onofrio, “Stability properties of pulse vaccination strategy in SEIR epidemic model,” Mathematical Biosciences, vol. 179, no. 1, pp. 57–72, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. K. Hale and A. S. Somolinos, “Competition for fluctuating nutrient,” Journal of Mathematical Biology, vol. 18, no. 3, pp. 255–280, 1983.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. B. Hsu, “A competition model for a seasonally fluctuating nutrient,” Journal of Mathematical Biology, vol. 9, no. 2, pp. 115–132, 1980.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. Lakmeche and O. Arino, “Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 7, no. 2, pp. 265–287, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetV. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, New Jersey, 1989.
View at: Zentralblatt MATH | MathSciNetP. Lenas and S. Pavlous, “Coexistence of three competing microbial populations in a chemostat with periodically varying dilution rate,” Mathematical Biosciences, vol. 129, no. 2, pp. 111–142, 1995.
View at: Publisher Site | Google ScholarJ. C. Panetta, “A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competitive environment,” Bulletin of Mathematical Biology, vol. 58, no. 3, pp. 425–447, 1996.
View at: Publisher Site | Google ScholarS. 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.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. G. Roberts and R. R. Kao, “The dynamics of an infectious disease in a population with birth pulses,” Mathematical Biosciences, vol. 149, no. 1, pp. 23–36, 1998.
View at: Publisher Site | Google ScholarB. Shulgin, L. Stone, and Z. Agur, “Pulse vaccination strategy in the SIR epidemic model,” Bulletin of Mathematical Biology, vol. 60, no. 6, pp. 1123–1148, 1998.
View at: Publisher Site | Google ScholarH. L. Smith, “Competitive coexistence in an oscillating chemostat,” SIAM Journal on Applied Mathematics, vol. 40, no. 3, pp. 498–522, 1981.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Y. Tang and L. S. Chen, “Density-dependent birth rate, birth pulses and their population dynamic consequences,” Journal of Mathematical Biology, vol. 44, no. 2, pp. 185–199, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet