On the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$

Authors

  • C. M. Kent Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, P. O. Box 842014, Richmond, Virginia 23284-2014 USA.
  • W. Kosmala Department of Mathematical Sciences, Appalachian State University, Boone, North Carolina 28608 USA.
Abstract:

We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

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on the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$

we investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  in particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

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volume 2  issue 2

pages  24- 43

publication date 2011-06-01

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