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 one predator system where the prey species follow Lotka-Volterra-type dynamics and the predator uptake functions are ratio dependent. We have derived the conditions for existence of different boundary equilibria and discussed their global behaviour. The sufficient condition for permanent co-existence of all the species is derived. Finally, we have discussed the possibility of extinction of the species from the system.

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