Global Dynamics of Three Anticompetitive Systems of Difference Equations in the Plane

Authors

M. DiPippo
Mustafa Kulenovic, University of Rhode IslandFollow

Document Type

Article

Date of Original Version

2013

Abstract

We investigate the global dynamics of several anticompetitive systems of rational difference equations which are special cases of general linear fractional system of the forms

Χ_n+1 = (α₁ + β₁ χ_n + y₁y_n)(A₁ + B₁x_n + C₁y_n), y_n+1 = (α2 + β₂x_n + y₂y_n)/(A₂ + B₂x_n + C₂y_n), n = 0, 1,…, where all parameters and the initial conditions x₀, y₀ are arbitrary nonnegative numbers, such that both denominators are positive. We find the basins of attraction of all attractors of these systems.

Citation/Publisher Attribution

M. DiPippo and M. R. S. Kulenović, “Global Dynamics of Three Anticompetitive Systems of Difference Equations in the Plane,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 751594, 11 pages, 2013. https://doi.org/10.1155/2013/751594.

Available at: http://dx.doi.org/10.1155/2013/751594

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.