Global Dynamic Scenarios for Competitive Maps in the Plane

Authors

Elliott Bertrand, University of Rhode Island
M. R. S. Kulenović, University of Rhode IslandFollow

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 x_n and increasing in the variable x_n-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.

Citation/Publisher Attribution

Bertrand, E., Kulenović, M.R.S. Global dynamic scenarios for competitive maps in the plane. (2018) Advances in Difference Equations, 2018(1), art. no. 291. DOI: 10.1186/s13662-018-1750-4

Available at: http://dx.doi.org/10.1186/s13662-018-1750-4

Creative Commons License

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