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Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield

Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield
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摘要 In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nutrient refilling and the periodic antibiotic injection occur with the same periodicity, but not simultaneously. The model is then formulated in terms of autonomous differential equations subject to impulsive perturbations. It is observed that either the population of microorganisms essentially washes out, or more favorably, the system is permanent. To describe this dichotomy, some biologically significant integral conditions are introduced. Further, it is shown that in a certain critical situation, a nontriviai periodic solution emerges via a bifurcation phenomenon. Finally, the dynamics of the model is illustrated with numerical experiments and computer simulations. In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nutrient refilling and the periodic antibiotic injection occur with the same periodicity, but not simultaneously. The model is then formulated in terms of autonomous differential equations subject to impulsive perturbations. It is observed that either the population of microorganisms essentially washes out, or more favorably, the system is permanent. To describe this dichotomy, some biologically significant integral conditions are introduced. Further, it is shown that in a certain critical situation, a nontriviai periodic solution emerges via a bifurcation phenomenon. Finally, the dynamics of the model is illustrated with numerical experiments and computer simulations.
出处 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第7期933-944,共12页 应用数学和力学(英文版)
基金 supported by the grant (No.623-2008-7179) for a postdoctoral position in Sweden awarded by the Swedish Research Council the National Natural Science Foundation of China (No.10771104) the High-Level Talent Project of Jiangsu University(No.08JDG047) supported by the grant funded by CNCSIS of Romania (No.342/2008) supported by Ministerio de Educación y Ciencia and FEDER,project MTM2007-61724 Xunta de Galicia and FEDER,project PGIDIT05PXIC20702PN
关键词 CHEMOSTAT impulsive differential equation PERMANENCE EXTINCTION fixedpoint approach BIFURCATION chemostat, impulsive differential equation, permanence, extinction, fixedpoint approach, bifurcation
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