Dynamics of the complex rational delay recursive sequence $\displaystyle{z_{n+1}=\frac{α+βz_{n-k}}{γ- z_{n}}}$

Sk. Sarif Hassan

paper

Dynamics of the complex rational delay recursive sequence $z_{n + 1} = \frac{α + β z _{n - k}}{γ - z _{n}}$

arXiv:1606.08887

Abstract

Dynamics of the delay rational difference equation $z_{n + 1} = \frac{α + β z _{n - k}}{γ - z _{n}}$ with complex parameters $α$ , $β$ , $γ$ 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.

Primary Draft

Dynamics of the complex rational delay recursive sequence zn+1​=γ−zn​α+βzn−k​​

Abstract

Dynamics of the complex rational delay recursive sequence $z_{n + 1} = \frac{α + β z _{n - k}}{γ - z _{n}}$