Dynamics and Bifurcation of a Second Order Quadratic Rational Difference Equation
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
References
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