A note on the energy transfer in coupled differential systems

We study the energy transfer in the linear system \begin{document}$ \begin{cases} \ddot u+u+\dot u = b\dot v\\ \ddot v+v-\epsilon \dot v = -b\dot u \end{cases} $\end{document} made by two coupled differential equations, the first one dissipative and the second one antidissipative. We see how the competition between the damping and the antidamping mechanisms affect the whole system, depending on the coupling parameter \begin{document}$ b $\end{document} .