Document Type
Article
Date of Original Version
2020
Abstract
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.
Citation/Publisher Attribution
Toufik Khyat, M. R. S. Kulenović, "Global Dynamics of Delayed Sigmoid Beverton–Holt Equation", Discrete Dynamics in Nature and Society, vol. 2020, Article ID 1364282, 15pages, 2020. https://doi.org/10.1155/2020/1364282
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.