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In this paper, certain dynamic scenarios for general competitive maps in the plane are presented and applied to some cases of second-order difference equation xn+1 = f(xn , xn− 1), n = 0, 1, . . ., where f is decreasing in the variable xn and increasing in the variable xn− 1. As a case study, we use the difference equation xn+1 =(x2n− 1 /(cx2n− 1 + dxn + f)), n = 0, 1, . . ., where the initial conditions x− 1 , x0 ≥ 0 and the parameters satisfy c, d, f > 0. In this special case, we characterize completely the global dynamics of this equation by finding the basins of attraction of its equilibria and periodic solutions. We describe the global dynamics as a sequence of global transcritical or period-doubling bifurcations.

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This work is licensed under a Creative Commons Attribution 4.0 License.