Global Asymptotic Stability in a Class of Difference Equations
نویسندگان
چکیده
منابع مشابه
Global Asymptotic Stability in a Class of Difference Equations
We study the difference equation xn = [( f × g1 + g2 +h)/(g1 + f × g2 +h)](xn−1, . . . ,xn−r), n = 1,2, . . . , x1−r , . . . ,x0 > 0, where f ,g1,g2 : (R+) → R+ and h : (R+) → [0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui} ≤ f (u1, . . . ,ur) ≤ max1≤i≤r{ui,1/ui}, (u1, . . . ,ur) T ∈ (R+) . We prove that this difference equation admits c = 1 as the globally asymptotically stable equi...
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1 College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 2 Key Laboratory of Network Control & Intelligent Instrument, Chongqing University of Posts and Telecommunications, Ministry of Education, Chongqing 400065, China 3 College of Applied Sciences, Beijing University of Technology, Beijing 100124, China 4 School of Communication and I...
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It was conjectured that for every integer m 3 the unique equilibrium c = 1 of the generalized Putnam equation xn+1 = ∑m−2 i=0 xn−i + xn−m+1xn−m xnxn−1 + ∑m i=2 xn−i , n= 0,1,2, . . . , with positive initial conditions is globally asymptotically stable. In this paper, we prove this conjecture. © 2005 Elsevier Inc. All rights reserved.
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2007
ISSN: 1687-1847
DOI: 10.1155/2007/16249