Mathematical models are important tools for analyzing ecological models. The dynamic relationship between prey and predators is one of the prevailing issues in mathematical ecology [?, ?, ??, ??, ??, ??, ??, ??]. The most common method of modelling ecological interactions consists of two differential equations with simple correspondence between the consumption of prey by the predator and the population’s growth. The traditional predator-prey models have been studied extensively [?, ??, ??, ??, ??]. Yodziz [??] proposed the following model to describe the interaction of predators and their prey: \\begin{align*} \\left\\{\\begin{array}{l} \\dot{P}=f(P)-UF(P,U),\\\\ \\dot{U}=UG(P,U), \\end{array}\\right. \\end{align*} where P(t) and U(t) represent the prey and predators densities at time t, respectively; the function f = f(P) characterizes the growth rate of the prey population in the absence of predator.
