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) - beta(1)(k)x(3)(k)}, x(3)(k + 1) = x(3)(k) exp{d(k) - e(k)x(3)(k) - beta(2)(k)x(2)(k)}. The sufficient and realistic conditions are obtained for the existence of a positive periodic solution of this system. (c) 2007 Elsevier Ltd. All rights reserved.