Document Type
Article
Date of Original Version
1-1-2018
Abstract
We investigate the global asymptotic stability of the following second order rational difference equation of the form xn+1=Bxnxn-1+F/bxnxn-1+cxn-12, n=0,1,., where the parameters B, F, b, and c and initial conditions x-1 and x0 are positive real numbers. The map associated with this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric space. In some cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability. Also, we show that considered equation exhibits the Naimark-Sacker bifurcation resulting in the existence of the locally stable periodic solution of unknown period.
Publication Title, e.g., Journal
Discrete Dynamics in Nature and Society
Volume
2018
Citation/Publisher Attribution
Kulenović, M. R., S. Moranjkić, M. Nurkanović, and Z. Nurkanović. "Global asymptotic stability and naimark-sacker bifurcation of certain mix monotone difference equation." Discrete Dynamics in Nature and Society 2018, (2018). doi: 10.1155/2018/7052935.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.