Local stability analysis of ratio-dependent predator–prey models with predator harvesting rates

We study the local stability of ratio-dependent predator–prey models with nonconstant predator harvesting rates. We provide more general conditions on the parameters involved in the models under which the models are locally stable or unstable at the two positive equilibria. We show that the predator free positive equilibrium can be a stable node or saddle-node and the positive interior equilibrium can be a stable or unstable node or focus or a center point depending on the ranges of the parameters involved. Our results generalize and improve some known results and show that the models have more rich dynamics than those ratio-dependent predator–prey models without any harvesting rates.