Dynamics and Bifurcation of a Second Order Quadratic Rational Difference Equation

Authors : Shahd HERZALLAH, Mohammad SALEH

Pages : 102-119

Doi:10.33187/jmsm.748724

View : 21 | Download : 8

Publication Date : 2020-12-29

Article Type : Research Paper

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