Mathematical Analysis of a Three-Tiered Model of Anaerobic Digestion

In this paper, we are interested in a mechanistic model describing the anaerobic mineralization of chlorophenol three-step food web. The is six-dimensional system ordinary differential equations. our study, take into account phenol and hydrogen input concentrations as well maintenance terms. Moreover, consider case large class growth rates, instead specific kinetics. general case, recent study shows that can have up to eight steady states, their existence conditions were analytically determined. We focus here on necessary sufficient local stability according four operating parameters process, which dilution rate chlorophenol, phenol, concentrations. previous studies, analysis was performed only numerically. Using Liénard--Chipart criterion, show positive state be unstable give numerical evidence for supercritical Hopf bifurcation with appearance stable periodic orbit. two diagrams respect rate, first, then concentration bifurcating parameters, showing present rich behavior, including bistability, coexistence, occurrence limit cycle.