On the global asymptotic stability of a second-order system of difference equations. (English) Zbl 1161.39013

Yalcinkaya, Ibrahim

Discrete Dyn. Nat. Soc. 2008, Article ID 860152, 12 p. (2008).

A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations \(z_{n+1}=(t_nz_{n-1}+a)/(t_n+z_{n-1})\), \(t_{n+1}=(z_nt_{n-1}+a)/(z_n+t_{n-1})\), \(n=0,1,2,\dots\), where the parameter \(a\in(0,\infty)\) and the initial values \((z_k,t_k)\in(0,\infty)\) (for \(k=-1,0)\).

MSC:

39A11	Stability of difference equations (MSC2000)
39A20	Multiplicative and other generalized difference equations

Keywords:

rational difference equations; global asymptotic stability; system of difference equations

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