Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation
نویسندگان
چکیده
منابع مشابه
Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation
We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: yn 1 r pyn yn−k / qyn yn−k , n ∈ N0, where the parameters p, q, r ∈ 0,∞ , k ∈ {1, 2, 3, . . .} and the initial conditions y−k, . . . , y0 ∈ 0,∞ . We show that the unique positive equilibrium of this equation is ...
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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)...
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ژورنال
عنوان ژورنال: Discrete Dynamics in Nature and Society
سال: 2010
ISSN: 1026-0226,1607-887X
DOI: 10.1155/2010/610467