Latest News

About CAMQ

Information for Authors

Editorial Board

Browse CAMQ Online

Subscription and Pricing

CAMQ Contacts

CAMQ Home

 

Volume 7,     Number 3,     Fall 1999

 

COMPETITION BETWEEN PLASMID-BEARING
AND PLASMID-FREE MICROORGANISMS IN A
CHEMOSTAT WITH DISTINCT REMOVAL RATES
BINGTUAN LI, YANG KUANG AND HAL L. SMITH

Abstract. In this paper we consider a competition model between plasmid-bearing and plasmid-free organisms in a chemostat that incorporates both general response functions and distinct removal rates. The model with identical removal rates was proposed in a paper of Stephanopoulis and Lapidus, and the analysis there was local. The complete global analysis of the model in the case of identical removal rates was given in a paper of Hsu, Waltman and Wolkowicz. However, it is important to consider the more general situation that removal rates are distinct. The object of this paper is to provide local and global analysis of the model in the case of different removal rates. When removal rates are different, the conservation law fails. To overcome this difficulty, we make use of a novel way of constructing Liapunov function in the study of the global stability of the steady state where the plasmid-bearing microorganism is absent. Local and global stability of other steady states, persistence analysis, as well as numerical simulations are also presented. Our findings are largely in line with that of the identical removal rate case.

 

Download PDF Files
 
(Subscribers Only)

© 2005, Canadian Applied Mathematics Quarterly (CAMQ)