ScienceAsia 12 (1986): 171-186 |doi: 10.2306/scienceasia1513-1874.1986.12.171

THE EFFECT OF THE SPECIFIC GROWTH RATES AND THE YIELD EXPRESSIONS ON OSCILLATIONS IN A TWO-TANK FERMENTOR

YONGWIMON LENBURY^a,c AND PHILIP CROOKE^b

ABSTRACT: Oscillations in the cells and substrate concentration in a two-tank continuous fermentation system are shown to be Hopf bifurcation in the underlying system of four ordinary differential equations. It is shown that. if other parameters are suitably fixed and the first tank yield is assumed constant. then a low first tank yield will result in a Hopf bifurcation to a periodic solution to the system. On the other hand, if the first yield depends linearly on the substrate level a more complex situation may develop. When the bifurcation parameter under consideration varies beyond a certain value. the existing periodic solution becomes unstable and a secondary bifurcation from this periodic solution occurs. This leads to an appearance of solutions on a torus in the four dimensional phase plane.

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a Department of Physics & Mathematics, Faculty of Sciences. Mahidol University, Rama 6. Rd. Bangkok 10400, Thailand.
b Department of Mathematics. Vanderbilt University. Nashville. TN 37235. U.S.A.
c To whom correspondence should be addressed.

Received 3 June 1986