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Dynamics of a rational difference equation using both theoretical and computational approaches. (English) Zbl 1085.39006
The authors study the global behavior of the difference equation x n +1=(p+x n )(x n +qx n-k ) -1 ,k{1,2,}, where the initial conditions x k ,x k +1,,x 0 are non-negative and the parameters p and q are also non-negative. They investigate the oscillatory character, invariant intervals, the boundedness and the global stability of the solutions of the above equation. The analysis of semi cycles is verified under some specific conditions posed on the coefficients. Finally, the authors give some numerical examples to support their theoretical discussions.
39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations
65Q05Numerical methods for functional equations (MSC2000)