PERMANENCE, AVERAGE PERSISTENCE AND EXTINCTION IN NONAUTONOMOUS SINGLE-SPECIES GROWTH CHEMOSTAT MODELS

Mehbuba Rehim () and Zhidong Teng ()
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Mehbuba Rehim: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Zhidong Teng: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

Advances in Complex Systems (ACS), 2006, vol. 09, issue 01n02, 41-58

Abstract: Non-autonomous single-species growth chemostat models with general response functions are considered. In the models, the dilution rate and removal rate are allowed to be different from each other. A series of new criteria on the boundedness, permanence, persistence, average persistence and extinction of the population is established. In particular, when models degenerate into the almost periodic case, the equivalences of the permanence, persistence and average persistence of species are obtained. These results improve and extend some well-known corresponding results obtained in Refs. 1, 14 and 17.

Keywords: Nonautonomous model; chemostat; boundedness; permanence; persistence; average persistence; extinction; removal rate; dilution rate; almost periodic model (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219525906000616

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