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.


39A11 Stability of difference equations (MSC2000)
39B05 General theory of functional equations and inequalities
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.