Stability of the Recursive Sequence xn+1=(α−βxn)/(γ+xn−1)
نویسندگان
چکیده
منابع مشابه
on the global asymptotic stability for a rational recursive sequence
the main objective of this paper is to study the boundedness character, the periodicity character, the convergenceand the global stability of the positive solutions of the nonlinear rational difference equation/ , n 0,1,2,....0 01 kii n ikin i n i x x b xwhere the coefficients i i b , , together with the initial conditions ,.... , , 1 0 x x x k are arbitrary...
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For all values of the parameter γ, (1.1) has a unique positive equilibrium x̄ = (γ + 1)/2. When 0 < γ < 1, the positive equilibrium x̄ is locally asymptotically stable. In the case where γ = 1, the characteristic equation of the linearized equation about the positive equilibrium x̄ = 1 has three eigenvalues, one of which is −1, and the other two are 0 and 1/2. In addition, when γ = 1, (1.1) posses...
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The paper considers the boundedness character of positive solutions of the difference equation xn+1 = A+ x n /x n−1, n ∈ N0, where A, p, and r are positive real numbers. It is shown that (a) If p2 ≥ 4r > 4, or p ≥ 1 + r, r ≤ 1, then this equation has positive unbounded solutions; (b) if p2 < 4r, or 2 √ r ≤ p < 1+ r, r ∈ (0,1), then all positive solutions of the equation are bounded. Also, an an...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2001
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7481