Quantitative bounds for the recursive sequence yn = A + yn / (yn-k)
نویسندگان
چکیده
This note provides new quantitative bounds for the recursive equation yn+1 = A + yn yn−k , n = 0, 1, . . . , where y−k , y−k+1, . . . , y−1, y0, A ∈ (0,∞) and k ∈ {2, 3, 4, . . .}. Issues regarding exponential convergence of solutions are also considered. In particular, it is shown that exponential convergence holds for all (A, k) for which global asymptotic stability was proven in [R.M. Abu-Saris, R. DeVault, Global stability of yn+1 = A + yn yn−k , Appl. Math. Lett. 16 (2) (2003) 173–178]. c © 2005 Elsevier Ltd. All rights reserved.
منابع مشابه
Quantitative Bounds for the Recursive Sequence y n + 1 = A +
This note provides new quantitative bounds for the recursive equation yn+1 = A + yn yn−k , n = 0, 1, . . . , where y−k, y−k+1, . . . , y−1, y0, A ∈ (0,∞) and k ∈ {2, 3, 4, . . .}. Issues regarding exponential convergence of solutions are also considered. In particular, it is shown that exponential convergence holds for all (A, k) for which global asymptotic stability was proven in R. M. Abu-Sar...
متن کاملOn a (2,2)-rational Recursive Sequence
We investigate the asymptotic behavior of the recursive difference equation yn+1 = (α+ βyn)/(1 + yn−1) when the parameters α < 0 and β ∈ R. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters α and β. We also give a summary of results and open questions on the more general recursive sequences yn+1 = (a+ byn)/(A+Byn−1), when th...
متن کاملOn the rational recursive sequence yn = A + yn-1/yn-m for small A
This work studies the existence of positive prime periodic solutions of higher order for rational recursive equations of the form yn = A + yn−1 yn−m , n = 0, 1, 2, . . . , with y−m , y−m+1, . . . , y−1 ∈ (0,∞) and m ∈ {2, 3, 4, . . .}. In particular, we show that for sufficiently small A > 0, there exist periodic solutions with prime period 2m +Um + 1, for almost all m, where Um = max{i ∈ N : i...
متن کاملOne-Shot Coupling for Certain Stochastic Recursive Sequences
We consider Markov chains {Γn} with transitions of the form Γn = f(Xn, Yn) Γn−1 + g(Xn, Yn), where {Xn} and {Yn} are two independent i.i.d. sequences. For two copies {Γn} and {Γn} of such a chain, it is well known that L(Γn)−L(Γn)⇒ 0 provided E[log(f(Xn, Yn))] < 0, where ⇒ is weak convergence. In this paper, we consider chains for which also ‖Γn − Γn‖ → 0, where ‖ · ‖ is total variation distanc...
متن کاملThe Global Attractivity of the Rational Difference Equation
This paper studies the behavior of positive solutions of the recursive equation yn = 1 + yn−k yn−m , n = 0, 1, 2, . . . , with y−s, y−s+1, . . . , y−1 ∈ (0,∞) and k,m ∈ {1, 2, 3, 4, . . .}, where s = max{k,m}. We prove that if gcd(k,m) = 1, with k odd, then yn tends to 2, exponentially. When combined with a recent result of E. A. Grove and G. Ladas (Periodicities in Nonlinear Difference Equatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 19 شماره
صفحات -
تاریخ انتشار 2006