The role of predator fertility and prey threshold bounds on the global and local dynamics of a predator-prey model with a prey out-flux dilution effect

The stability of a predator-prey model for an ecosystem faced with a prey out-flux which is analogous to and modelled as an Allee effect was investigated. Local and global stability conditions of positive steady states are highlighted in both qualitative and numerical results. The results highlight the bounds for the conversion efficiency of prey biomass to predator biomass (fertility gain) for which stability of the three species ecosystem model can be attained. Besides showing the occurrence under parameter space of the so-called paradox of enrichment, early indicators of chaos can also be deduced. Numerical results reveal stable oscillatory behaviours and stable spirals of the species as predator fertility rate, mortality rate and prey threshold are varied.