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Dynamics of the complex rational delay recursive sequence $\displaystyle{z_{n+1}=\frac{\alpha+\beta z_{n-k}}{\gamma - z_{n}}}$

Dynamical Systems 2016-06-30 v1

Abstract

Dynamics of the delay rational difference equation zn+1=α+βznkγzn\displaystyle{z_{n+1}=\frac{\alpha+\beta z_{n-k}}{\gamma - z_{n}}} with complex parameters α\alpha, β\beta, γ\gamma and arbitrary complex initial conditions is investigated. Existence of prime period two solutions and higher order periods are ensured in the complex parameters unlike in the case of real parameters of the same rational difference equation. In addition, a new dynamical behavior, chaotic solutions of the difference equation are ensured computationally.

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Cite

@article{arxiv.1606.08887,
  title  = {Dynamics of the complex rational delay recursive sequence $\displaystyle{z_{n+1}=\frac{\alpha+\beta z_{n-k}}{\gamma - z_{n}}}$},
  author = {Sk. Sarif Hassan},
  journal= {arXiv preprint arXiv:1606.08887},
  year   = {2016}
}

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