Multiple limit cycles in a continuous culture vessel with variable yield

Determining the number of limit cycles for a continuous culture vessel system is always useful in analyzing the system. We prove the conditions that guarantee there exist three limit cycles for the chemostat with variable yield that was first proposed by Huang Limit cycles in a continuous fermentation model, J. Math. Chem. 5 (1990) 287–296] and by Pilyugin and Waltman Multiple limit cycles in the chemostat with variable yield, Math. Boisci. 182 (2003) 151–166].