Abstract
The numerical investigation results of the dynamic behavior of an ethanol fermentor excited by external sinusoidal periodic perturbations are reported. The characteristics of the discriminant of the cubic polynomial of the steady state autonomous model of the unforced fermentor were used to divide the parameter space into regions with different number of steady state solutions. The bioethanol fermentor exhibits interesting complicated dynamic behavior when the center of forcing is close to a static limit point (SLP) i.e. the discriminant=0. Numerical simulations have presented evidence for the existence of multistability, bistability and bubbles phenomena in the forced bioethanol fermentor. This is - to the best of our knowledge - the first study that shows these phenomena in the forced bioethanol fermentor. Multistablity is characterized by the coexistence of several attractors. It has been shown that, the multistability exhibits the coexistence of three attractors, two of them are chaotic and one quasi-periodic, and the bistability exhibits the coexistence of two attractors, one of them is periodic and the other is either periodic, quasi-periodic or chaotic attractor. In the multistabiliy region, we have observed that changing the forcing amplitude with the sequence of events there is an appearance of the bistability and then a transition to multistabilty. It has been shown that, the bubble region acts as a period doubling killer, which has a lethal effect in killing the universal period doubling scenario to chaos by reversing the sequence to period halving. It is also shown that, the unforced (14.55% increase in ethanol average concentration relative to the steady state operation) or forced (8.87% increase in ethanol average concentration relative to the steady state operation) unsteady state operations give better fermentor performance than the steady state operations with respect to the average ethanol concentration and yield. The investigation shows that the nature and the position of the center of forcing have significant effect on the dynamic response of the periodically forced fermentors. It has been found that, the forcing could be beneficial or harmful to the fermentor performance depending on the position of center of forcing. The system shows interesting phase planes at certain forcing amplitudes.