# Rotation number of perturbated equation

I have a differential equation on torus $(t,x)$ and well studied it's Arnold tongues for Poincare map of the circle $x(t=0) \to x(t=2\pi)$. The question is how changes rotation number when I add small periodic perturbation to equation, for example $\varepsilon \sin 2x$? Is there any technic to give some prediction? Some info: equation is $\dot{x}=a+b \sin(t)+sin(x)$, its conjugated to Riccati equation (so perturbation of original equation is perturbation of Riccati equation)

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