Nonhomogeneous poisson nonlinear transformations on countable infinite set

In this paper, we construct the family of nonhomogeneous Poisson quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that nonhomogeneous Poisson quadratic stochastic operators are regular transformation