Local dynamics and global attractivity of a certain second-order quadratic fractional difference equation
نویسندگان
چکیده
منابع مشابه
Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation
We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x(n+1) = x²(n-1)/(ax²(n) + bx(n)x(n-1) + cx²(n-1)), n = 0,1, 2,…, where the parameters a, b, and c are positive numbers and the initial conditions x₋₁ and x₀ are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilib...
متن کاملThe Global Attractivity of a Higher Order Rational Difference Equation
This paper studies global asymptotic stability for positive solutions to the equation yn = yn−kyn−lyn−m + yn−k + yn−l + yn−m 1 + yn−kyn−l + yn−kyn−m + yn−lyn−m , n = 0, 1, . . . , with y−m, y−m+1, . . . , y−1 ∈ (0,∞) and 1 ≤ k < l < m. The paper also includes a listing of possible semi-cycle structures for various (k, l, m). The results generalize several others in the recent literature.
متن کاملGlobal attractivity of a higher-order nonlinear difference equation
In this paper, we investigate the global attractivity of negative solutions of the nonlinear difference equation xn+1 = 1− xn−k A + xn , n = 0, 1, . . . , where A ∈ (−∞, 0), k is a positive integer and initial conditions x−k, · · · , x0 are arbitrary real numbers. We show that the unique negative equilibrium of abovementioned equation is a global attractor with a basin under certain conditions....
متن کاملOn the global attractivity of difference equation of higher order
where a, b, c and d ∈ (0,∞) with the initial values x−p, x−p+1, ..., x−1 and x0 ∈ (0,∞), where p is a positive integer. Here, we recall some notations and results which will be useful in our investigation. Let I be some interval of real numbers and let F : I → I be a continuously differentiable function. Then for every set of initial values x−k, x−k+1, ..., x0 ∈ I, the difference equation (1.2)...
متن کاملGlobal dynamics of quadratic second order difference equation in the first quadrant
We investigate the global behavior of a quadratic second order difference equation xnþ1 1⁄4 Axn þ Bxnxn 1 þ Cx 2 n 1 þ Dxn þ Exn 1 þ F; n 1⁄4 0;1; . . . with non-negative parameters and initial conditions. We find the global behavior for all ranges of parameters and determine the basins of attraction of all equilibrium points. 2013 Elsevier Inc. All rights reserved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2014
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2014-68