Persistence of two prey-one predator system with ratio-dependent predator influence

In this study, we consider a mathematical model of two competing prey and o ne predator:system where the prey species follow Lotka-Volterra-type dynami cs and the predator uptake functions are ratio dependent. We have derived t he conditions for existence of different boundary equilibria and discussed their global behaviour. The sufficient condition for permanent co-existence of ail the species is derived. Finally, we have discussed the possibility of extinction of the species from the system. Copyright (C) 2000 John Wiley & Sons, Ltd.