I have non linear non-autonomous ODE system given by
$$\tilde{d}(t)=d-\frac{A \cos(t)}{\bar{A}+A \sin(t)}$$ $$\dot{x}(t)=-yx(1-x)F(y)$$ $$\dot{y}(t)=-(1-y)(3xy(1-y^4)-\tilde{d}(t))$$
where $F(y)$ is a non linear function of $y$ that is decreasing in $y$ for most of the domain.
I can solve this numerically using Matlab. Doing so, I get solutions for $x(t)$ and $y(t)$ that look periodic after some intial time span. Is there any way to make some statements about how ''average'' value of $x(t)$ changes with changing $A?$ Numerical solutions seem to suggest that it increases. $\tilde{d}(t)$ averaged over a cycle increases with A. I am very new to non-autonomous systems, so I would be very happy if one could guide me to the some concepts that may help me 'prove' this statement more formally.