A predator-prey model with ratio-dependent functional response and Strong Allee effect on prey

A ratio-dependent predator-prey model with strong Allee effect on prey is analyzed by making a parametric analysis of stability properties of dynamics on the system in which the functional response is a function of the ratio of prey to predator. It is shown that incorporating of Allee effect on prey equation significantly modifies the dynamics of the original system, as the modified model involves other non-topological equivalent behaviors. We prove the existence of a parameter subsets for which the system can have a Hopf bifurcation, a Bogdanov-Takens bifurcation, and showing the existence of separatrix curves in the phase plane determining that the long-term dynamics of the system is high sensitivity to initial conditions. Key–Words: Predator-prey, Ratio-dependent, Allee effect.