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On some systems of difference equations. (English) Zbl 1243.39009

The authors consider the following three systems of nonlinear difference equations

u n+1 =v n 1+v n ,v n+1 =u n 1+u n ,
u n+1 =v n 1+u n ,v n+1 =u n 1+v n ,


u n+1 =u n 1+v n ,v n+1 =v n 1+u n ,

where n 0 and the initial values u 0 and v 0 are given complex numbers. By help of the auxiliary Riccati equation

x n+1 =x n a+bx n ,a,b,n 0 ,

the general solution of each system is explicitly given. As a consequence, the asymptotic behaviour of the solutions is analysed in detail as n.

39A20Generalized difference equations
39A22Growth, boundedness, comparison of solutions (difference equations)
39A23Periodic solutions (difference equations)
39A30Stability theory (difference equations)
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