I have a system of nonlinear DEs $\dot{x}=f(x)$, where $x=[z_1,\,z_2,\,\phi_1,\,\phi_2]$. The r.h.s. are $2\pi$-periodic in $\phi_1$ and $\phi_2$, i.e. $f(x)$ contains the terms like $trig(\phi_1)*trig(\phi_2)$, where $trig$ is either sine or cosine.
When I simulate the system I observe a superposition of two oscillations with frequences $\omega_1$ and $\omega_2$, $\omega_1 \approx 7\omega_2$. I tried to average over $[0,2\pi]$, but the resulting system turned out to be too coarse. So, I wonder
Is it possible to separate the high- and low-frequency oscillations and average the system in order to get rid of the high-frequency ones?
I understand that the question can be too broad. If so, I would appreciate any references to the relevant sources of information.