Dynamics and Bifurcation of a Second Order Quadratic Rational Difference Equation

Year 2020, Volume: 3 Issue: 3, 102 - 119, 29.12.2020

Shahd Herzallah Mohammad Saleh

https://doi.org/10.33187/jmsm.748724

Cited By: 2

Abstract

In this paper, we study the dynamics and bifurcation of $$ x_{n+1} = \frac{\alpha+ \beta {x^2}_{n-1}}{A+B {x_n}+C{x^2}_{n-1}}, \ n=0,\ 1, \ 2, \ ... $$ with positive parameters $\alpha,\ \beta, \ A, \ B, \ C, $ and non-negative initial conditions. Among others, we investigate local stability, invariant intervals, boundedness of the solutions, periodic solutions of prime period two and global stability of the positive fixed points.

Keywords

Fixed point, Neimark-Sacker bifurcation, Stability

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