Theoretical analysis of ethanol fermentation with product inhibition and synchronous impulse

Abstract

In this paper, a universal model of ethanol fermentation with product inhibition and synchronous impulse is investigated. Firstly, continuous input substrate is taken. By using the qualitative theory of ordinary differential equations, we prove the complex dynamics of the equilibria. Moreover, synchronous impulse of input substrate is also considered. Using small amplitude perturbation, we obtain the biomass-free periodic solution is locally stable if some conditions are satisfied. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. The above results are validated by numerical simulations.