Global dynamics of a higher order difference equation with a quadratic term

Abstract

In this paper, we investigate the dynamics of the following higher order difference equation

$$\begin{aligned} x_{n+1}=A+B\frac{x_{n}}{x_{n-m}^{2}}, \end{aligned}$$

with AB and initial conditions are positive numbers, and \(m\in \left\{ 2,3,\cdots \right\} \). Especially we study the boundedness, periodicity, semi-cycles, global asymptotically stability and rate of convergence of solutions of related higher order difference equations.

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Correspondence to Erkan Taşdemir.

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Taşdemir, E. Global dynamics of a higher order difference equation with a quadratic term. J. Appl. Math. Comput. (2021). https://doi.org/10.1007/s12190-021-01497-x

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Keywords

  • Difference equations
  • Periodicity
  • Boundedness
  • Global stability
  • Semi-cycle
  • Rate of convergence

Mathematics Subject Classification

  • 39A10
  • 39A23
  • 39A30