In this paper we consider a difference equation of the form u ( t + 2 ) = α u ( t + 1 ) + β u ( t + 1 ) − α u ( t ) α u ( t ) , for - \infty$"> t > − ∞ , seems to be a general statement of a relative socio-spatial dynamics. Indeed this equation is one of “population model”. We investigate behavior of solutions and expression of analytic general solutions of this model.