- Journal of Mathematical Sciences and Modelling
- Vol: 3 Issue: 3
- Dynamics and Bifurcation of a Second Order Quadratic Rational Difference Equation
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 : 10 | Download : 3
Publication Date : 2020-12-29
Article Type : Research
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