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On the Behavior of Positive Solutions of a Difference Equations System xn+1={yn-2+yn-3}/xn, yn+1={xn-2+xn-3}/yn

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DOI: 10.4236/am.2013.49A003    2,973 Downloads   4,684 Views   Citations

ABSTRACT

Motivated by an open problem in the literature “Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture”, we introduce a difference equation system:

xn+1={yn-2+yn-3}/xn, yn+1={xn-2+xn-3}/yn , n=o, 1 ...* Where xi, yi ∈(0, ∞), i=-3, -2, -1, 0.

We try to find out some conditions such that the solution of system converges to periodic solution. This model can be applied to the two species competition and population biology.



Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

D. Zhang, W. Ji, L. Wang and X. Li, "On the Behavior of Positive Solutions of a Difference Equations System xn+1={yn-2+yn-3}/xn, yn+1={xn-2+xn-3}/yn," Applied Mathematics, Vol. 4 No. 9A, 2013, pp. 13-18. doi: 10.4236/am.2013.49A003.

References

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