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On the Dynamics of the Higher Order Nonlinear Rational Difference Equation |
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PP: 121-129 |
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Author(s) |
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M. A. El-Moneam,
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Abstract |
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| In this article, we study the periodicity, the boundedness and the global stability of the positive solutions of the following
nonlinear difference equation
xn+1 = Axn +Bxn−k +Cxn−l +Dxn−s +
bxn−k
[dxn−k −exn−l ]
, n = 0,1,2, .....,
where the coefficients A,B,C,D,b,d, e ∈ (0,¥), while k, l and s are positive integers. The initial conditions
x−s ,..., x−l ,..., x−k, ..., x−1, x0 are arbitrary positive real numbers such that k < l < s . Some numerical examples will be given
to illustrate our results. |
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