A note on the energy transfer in coupled differential systems

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