English

On the asymptotic stability of a rational multi-parameter first order difference equation

Dynamical Systems 2010-11-17 v2

Abstract

In this part we study the dynamics of the following rational multi-parameter first order difference equation x_{n+1} =(ax_{n}^3+ bx_{n}^2+cx_{n} + d)/x_{n}^3, x_{0}\in R^{+} where the parameters a, b, d together with the initial condition x_{0} are positive while the parameter c could accept some negative values. We investigate the equilibria and 2-cycles of this equation and analyze qualitative and asymptotic behavior of it's solutions such as convergence to an equilibrium or to a 2-cycle.

Keywords

Cite

@article{arxiv.1011.3503,
  title  = {On the asymptotic stability of a rational multi-parameter first order difference equation},
  author = {M. Shojaei},
  journal= {arXiv preprint arXiv:1011.3503},
  year   = {2010}
}

Comments

Submitted to Nonlinear Analysis:Real World Applications

R2 v1 2026-06-21T16:44:09.252Z