Global attractivity of the recursive sequence $$x_{n + 1} = \frac{{\alpha - \beta x_{n - k} }}{{\gamma + x_n }}

Our aim in this paper is to investigate the global attractivity of the recursive sequence $$x_{n + 1} = \frac{{\alpha - \beta x_{n - k} }}{{\gamma + x_n }},$$ where a, b, g >0 andk=1,2,... We show that the positive equilibrium point of the equation is a global attractor with a basin that depends...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2004-03, Vol.16 (1-2), p.243-249
Main Authors: El-Owaidy, H. M., Ahmed, A. M., Elsady, Z.
Format: Article
Language:English
Subjects:
Basins
Computation
Mathematical analysis
Mathematical models
Recursive
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Summary:Our aim in this paper is to investigate the global attractivity of the recursive sequence $$x_{n + 1} = \frac{{\alpha - \beta x_{n - k} }}{{\gamma + x_n }},$$ where a, b, g >0 andk=1,2,... We show that the positive equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients.
ISSN:1598-5865
1865-2085
DOI:10.1007/BF02936165