ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE





On the recursive system  
xn+1 = A + xn-m / yn,   yn+1 = B + yn-m / xn


Qianhong Zhang, Lihui Yang and Jingzhong Liu

Received: July 2, 2012;   Accepted: February 13, 2012



Abstract.   In this paper, we investigate the boundedness, persistence and global asymptotic stability of positive solutions of the system of two nonlinear difference equations

xn+1 = A + xn-m / yn,   yn+1 = B + yn-m / xn   n = 0, 1, . . .

where A, B Î (0,¥),   xi Î (0,¥),   yi Î (0,¥),   i = -m, -m+1, . . ., 0.  

Keywords:  difference equation; boundedness; persistence; global asymptotic stability.  

AMS Subject classification: Primary:  39A10.  


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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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