I'm working on a system of functional equations
$$\begin{align} Q'(t) &=-(\delta(t)+\beta(Q(t))Q(t)+2(1-K(t))e^{-\gamma(t)\tau}u(t-\tau) \tag{Eq1}\\[8pt] u(t) &=\beta(Q(t))Q(t)+2K(t)e^{-\gamma(t)\tau}u(t-\tau)\tag{Eq2} \end{align}$$
where $K$,$\gamma$ and $\delta$ are $T$-periodic functions. It cannot be put as an abstract ODE (at least I don't know how), but is still a dynamical system. I've proven the existence of a $T$ periodic solution using topological methods. Now I want to study the stability of such solution. Do you know if there is some kind of Floquet theory for abstract dynamical systems? Thanks!