Periodic solutions of a discrete two-species competitive model with stage structure

In this paper, we investigate the following discrete periodic stage-structure model. x 1 ( k + 1 ) = x 1 ( k ) exp { − a 1 ( k ) + b 1 ( k ) x 2 ( k ) x 1 ( k ) } , x 2 ( k + 1 ) = x 2 ( k ) exp { a 2 ( k ) x 1 ( k ) x 2 ( k ) − b 2 ( k ) − c ( k ) x 2 ( k ) − β 1 ( k ) x 3 ( k ) } , x 3 ( k + 1 ) = x 3 ( k ) exp { d ( k ) − e ( k ) x 3 ( k ) − β 2 ( k ) x 2 ( k ) } . The sufficient and realistic conditions are obtained for the existence of a positive periodic solution of this system.