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Journal of Mathematical Chemistry

, Volume 43, Issue 3, pp 1273–1284 | Cite as

Global stability of a three-dimensional bio-reactor with inhibition responses

  • Houqin Su
  • Xuncheng Huang
  • Xuncheng Huang
  • Xiaoning Xu
Article

A three-dimensional bio-reactor model of exploitative competition of two predator organisms with inhibition responses for the same renewable organism with reproductive properties is considered. By constructing a modified Lyapunov function and using LaSalle’s invariant principle, it is shown that the lower “break-even” concentration predator organism survives in the competition.

Keywords

global stability competition break-even Lyapunov function invariant principle 

AMS subject classifications

92A15 92A17 34C15 34C35 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Houqin Su
    • 1
  • Xuncheng Huang
    • 2
  • Xuncheng Huang
    • 3
  • Xiaoning Xu
    • 3
  1. 1.Donghua UniversityShanghaiChina
  2. 2.RDS Research Center, Infront CORPKearnyUSA
  3. 3.Yangzhou Polytechnic UniversityYangzhouChina

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