Global asymptotic stability of a second-order system of difference equations

Tran Hong Thai () and Vu Van Khuong ()
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Tran Hong Thai: Hung Yen University of Technology and Education
Vu Van Khuong: University of Transport and Communications

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 2, 185-198

Abstract: Abstract In this paper a sufficient condition is obtained for the global asymptotic stability of the following system of difference equations $$x_{n + 1} = \frac{{x_n y_{n - 1}^b + 1}} {{x_n + y_{n - 1}^b }}, y_{n + 1} = \frac{{y_n x_{n - 1}^b + 1}} {{y_n + x_{n - 1}^b }}n = 0,1,2 \ldots$$ where the parameter b ∈ [0, ∞) and the initial values (x k , y k ) ∈ (0, ∞) (for k = −1, 0).

Keywords: Rational difference equations; system; global asymptotic stability; equilibrium point; semicycle (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s13226-014-0058-7

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