Positive periodic solutions of a discrete mutualism model with time delays

where ri,Ki,αi ∈ C(R,R+), αi > Ki, i = 1,2, τi,σi ∈ C(R,R+), i = 1,2, ri, Ki, αi, τi, σi(i = 1,2) are functions of period ω > 0. Since the study on periodic solutions of a population model is of great interest in mathematical biology [5] and many authors [1, 7] have argued that the discrete-time models governed by difference equations are more appropriate than the continuous ones when the populations have nonoverlapping generations, then, discrete-timemodels can provide efficient computational types of continuousmodels for numerical simulations. It is reasonable to study the discrete-timemutualismmodel governed by difference equations. One of the ways of deriving difference equations modeling the dynamics of populations with nonoverlapping generations is based on appropriate modifications of the corresponding models with overlapping generations [2, 4]. In this approach, differential equations with piecewise constant arguments have been proved to be useful. Following the same idea and the same method in [2, 4], one can easily derive the following discrete