Logistic growth functions may overcome extinction in a ratio-dependent predator-prey model: deterministic and stochastic approach

Abstract

Ratio-dependent predator-prey models are increasingly favoured by ecologists as an alternative or more suitable ones for predator-prey interaction where predation involves searching process. Ratio-dependent models set up a challenging issue regarding their dynamics near the origin. This is due to the fact that such models are undefined at (0, 0). We study the analytical behavior at (0, 0) for a ratio-dependent predator-prey model by taking the logistic form of growth function for predator as well as prey population. This point is not a global attractor. On the otherhand the interior equilibrium point is locally as well as globally asymptotically stable in some region of parametric space. This result contradicts the result of Jost et. al. (1999) and supports the result of Getz (1984). Stochastic stability of the system around positive interior equilibrium is studied. To substantiate our analytical findings numerical simulations are carried out for hypothetical set of parameter values.