Dynamical Behavior of a Stochastic Ratio-Dependent Predator-Prey System

Ecological systems are mainly characterized by the interaction between species and their surrounding natural environment 1 . Especially, the dynamic relationship between predators and their preys has long been and will continue to be one of the dominant themes in both ecology and mathematical ecology, due to its universal existence and importance 2– 4 . The interaction mechanism of predators and their preys can be described as differential equations, such as Lotaka-Volterra models 5 . Recently, many researchers pay much attention to functional and numerical responses over typical ecological timescales, which depend on the densities of both predators and their preys most likely and simply on their ration 6–8 . Such a functional response is called a ratio-dependent response function, and these hypotheses have been strongly supported by numerous and laboratory experiments and observations 9–11 . It is worthy to note that, based on the Michaelis-Menten or Holling type II function, Arditi and Ginzburg 6 firstly proposed a ratio-dependent function of the form