کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4636866 | 1340729 | 2006 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Global stability of a higher order rational recursive sequence Global stability of a higher order rational recursive sequence](/preview/png/4636866.png)
In this paper, we study the qualitative behavior of solutions of the class of delay difference equationxn+1=βxn-k+1+γxn-2k+1A+Bxn-k+1,n=0,1,2,…,where the initial conditions x−2k+1, … , x−1, x0 are positive, k ∈ {1, 2, …}, and the parameters β, γ, A, B are positive. Our concentration is on invariant intervals and the global stability of the above mentioned equation. We obtain sufficient conditions for the global attractivity of all positive solutions about the zero and positive equilibrium points with basins that depend on specific conditions posed on the coefficients. Furthermore, the oscillation and the character of semicycles about the positive equilibrium are thoroughly discussed. It is also illustrated that for some special case of parameters, the solution will be either a period-2 solution, or will converge to the equilibrium point, or will have unbounded solutions.
Journal: Applied Mathematics and Computation - Volume 179, Issue 1, 1 August 2006, Pages 161–174