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1. 4. 2016.
Global Dynamics and Bifurcations of Certain Second Order Rational Difference Equation with Quadratic Terms
We investigate global dynamics of the equation $$\begin{aligned} x_{n+1}=\frac{x_{n-1}}{ax_{n}^{2}+ex_{n-1}+f},\quad n=0,1,2,\ldots , \end{aligned}$$xn+1=xn-1axn2+exn-1+f,n=0,1,2,…,where the parameters a, e and f are nonnegative numbers with condition $$a+e+f>0$$a+e+f>0 and the initial conditions $$x_{-1},x_{0}$$x-1,x0 are arbitrary nonnegative numbers such that $$x_{-1}+x_{0}>0$$x-1+x0>0. The global dynamics of this equation consists of three bifurcations, two exchange of stability bifurcations and one global period doubling bifurcation.