I posted this problem before in MO but only I would like to know if this difference equation :$$x_{n+1}=Ax^2_{n}-Bx^2_{n-1}$$ where $A(\theta)= \cos(\theta)$ and $B(\theta) =\sin(\theta)$ are nonnegative parameters and $x_{-1}$, $x_0$ are nonnegative initial conditions with $x_{-1}+x_{0}>0$ was studied before (Global behavior and boundedness of its solutions).
Are there any references or books discussing it?