Document Type

Article

Date of Original Version

8-28-2018

Department

Mathematics

Abstract

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 xn+1= Cx2 n-1 + Exn-1 ________________ , n=0,1,..., ax2n + dxn +f 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.

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