Stability and bifurcation control for a fractional-order chemostat model with time delays and incommensurate orders.

In this paper, a delayed fractional Lotka-Volterra food chain chemostat model with incommensurate orders is proposed, and the effect on system stability and bifurcation of this model are discussed. First, for the system with no controller, the stability and Hopf bifurcation with respect to time delay are investigated. Taking the time delay as the bifurcation parameter, the relevant characteristic equations are analyzed, and the conditions for Hopf bifurcation are proposed.

Arthrobacter is a universal responder to di-n-butyl phthalate (DBP) contamination in soils from various geographical locations.

Plasticizer phthalic acid esters (PAEs) are commonly found as contaminants in various soils. Previous studies indicated that their natural degradation can substantially differ among soil types; however, potential implications of the soil microbiome remained largely unexplored. Here, we have collected ten soil types from nine different geographical regions of China to investigate the degradation of DBP therein and role of bacteria in this process.