Local Dynamics and Global Stability of Certain Second-Order Rational Difference Equation with Quadratic Terms

Authors

S. Jasarevic Hrustic
Mustafa Kulenovic, University of Rhode IslandFollow
M. Nurkanovic

Document Type

Article

Date of Original Version

2016

Abstract

We present a complete local dynamics and investigate the global dynamics of the following second-order difference equation: x_n+1 = (Ax² + Ex_n-1 + F) / (ax_n² + ex_n-1 + f), n = 0, 1, 2, . . ., where the parameters A, E, F, a, e, and f are nonnegative numbers with condition A + E + F > 0, a + e + f > 0, and initial conditions x_-1, x₀ are arbitrary nonnegative numbers such that ax_n² + ex_n-1 + f > 0, n = 0, 1, 2, . . . .

Citation/Publisher Attribution

S. Jašarević Hrustić, M. R. S. Kulenović, and M. Nurkanović, “Local Dynamics and Global Stability of Certain Second-Order Rational Difference Equation with Quadratic Terms,” Discrete Dynamics in Nature and Society, vol. 2016, Article ID 3716042, 14 pages, 2016. doi:10.1155/2016/371604

Available at: http://dx.doi.org/10.1155/2016/371604

Creative Commons License

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