  The mathematical analysis of a three-tiered food-web describing anaerobic
chlorophenol mineralisation has suggested the emergence of interesting
dynamical behaviour through its specific ecological interactions, which include
competition, syntrophy and product inhibition. Previous numerical analyses have
revealed the possibility for a Hopf bifurcation occurring through the interior
equilibrium and the role of extraneous substrate inputs in both mitigating the
emergence of periodic solutions and expanding the desired stable positive
steady-state, where full mineralisation occurs. Here we show that, for a
generalised model, the inflow of multiple substrates results in greater
dynamical complexity and prove the occurrence of a supercritical Hopf
bifurcation resulting from variations in these operating parameters. Further,
using numerical estimation, we also show that variations in the dilution rate
can lead to Bogdanov-Takens and Bautin bifurcations. Finally, we are able to
show apply persistence theory for a range of parameter sets to demonstrate
unique persistence in the cases where chlorophenol and hydrogen are
extraneously added to the system, mirroring recent applied studies highlighting
the role of hydrogen in maintaining stable anaerobic microbial communities.
