DYNAMIC BEHA VIOR OF A MEMBRANE PERMEABILITY SENSITIVE MODEL FOR A CONTINUOUS BIO-REACTOR EXHIBITING CULTURE RHYTHMICITY

YONGWIMON LENBURY AND SOMSAK ORANKITJAROEN

ABSTRACT: A modified Monod model of a continuous microbial culture in which the yield term depends linearly on the substrate concentration is extended to incorporate the effect of external forces on the cell membrane permeability. Bifurcation analysis of the new mathematical model, which consists of three non-linear ordinary differential equations, shows that the model can simulate the oscillatory behavior observed in experimental data for certain ranges of the system parameters. Computer simulation of the model is presented in support of our theoretical predictions.

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Department of Mathematics, Faculty of Science, Mahidol University, Rama 6 Rd., Bangkok 10400, Thailand.

Received April 3, 1995