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Volume 9,     Number 3,     Fall 2001

 

GLOBAL STABILITY OF CHEMOSTAT MODELS INVOLVING TIME DELAYS AND ZONES OF NO ACTIVATION
V. SREE HARI RAO AND P. RAJA SEKHARA RAO

Abstract. A chemostat model with distributed time delays in both nutrient recycling and biotic species growth is considered. In this paper we introduce a new notion relating to the nonconsumption of nutrient by the consumer at the equilibrium value and this new notion is termed as 'zone of no activation.' This may also be viewed as a measure of restoring stability, especially when excess consumption of the nutrient drives the system to instability. The influence of zones of no activation on the global asymptotic stability of the positive equilibrium solution of the model equations is discussed in detail. It is found that the criteria obtained in this paper are easily verifiable and actually independent of each other. Further, the asymptotic nature of solutions, in the event of the model not possessing a positive equilibrium is also discussed.

 

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