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A coupled system of rational difference equations. (English) Zbl 1001.39017
For the solutions of $$x_{n+1}=x_n/(a+cy_n),$$ $$y_{n+1}=y_n/(b+dx_n)$$, $$n\in \mathbb N_0$$, with positive $$a,b,c,d$$ and non-negative $$x_0$$, $$y_0$$ the asymptotic behaviour and the global stability properties are investigated.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39B05 General theory of functional equations and inequalities
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##### References:
 [1] D. Clark, M.R.S. Kulenovic and J.F. Selgrade, Global asymptotic behavior of xn+1 = xn/(a + cyn), yn+1 = yn/(b + dxn) (to appear). [2] Elaydi, S., Discrete chaos, (2000), Chapman and Hall/CRC Boca Raton, FL · Zbl 0945.37010 [3] Franke, J.E.; Yakubu, A., Mutual exclusion versus coexistence for discrete competitive systems, J. math. biol., 30, 161-168, (1991) · Zbl 0735.92023 [4] Selgrade, J.F.; Ziehe, M., Convergence to equilibrium in a genetic model with differential viability between the sexes, J. math. biol., 25, 477-490, (1987) · Zbl 0634.92008 [5] Smith, H.L., Planar competitive and cooperative difference equations, J. diff. equa. appl., 3, 335-357, (1998) · Zbl 0907.39004 [6] Hale, J.; Kocak, H., Dynamics and bifurcations, (1991), Springer-Verlag New York · Zbl 0745.58002 [7] Robinson, C., Stability, symbolic dynamics, and chaos, (1995), CRC Press Boca Raton, FL · Zbl 0853.58001 [8] Lakshmikantham, V.; Triggiante, D., Theory of difference equations, (1988), Academic Press Boston, MA
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