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In this paper we present some global dynamic scenarios for general competitive maps in the plane. We apply these results to the class of second-order autonomous difference equations whose transition functions are decreasing in the variable xn and increasing in the variable xn-1. We illustrate our results with the application to the difference equation

[Mathematical equations cannot be displayed here, refer to PDF]

where the initial conditions x-1 and x0 are arbitrary nonnegative numbers such that the solution is defined and the parameters satisfy C, E, a, d, f ≥ 0, C + E > 0, a + C > 0, and a + d > 0. We characterize the global dynamics of this equation with the basins of attraction of its equilibria and periodic solutions.

Creative Commons License

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