Before revision:  The results are applied to the Repressilator in synthetic biology, where hyperbolic instability of a unique equilibrium guarantees the persistence of oscillation phenomena in the global sense, and the effectiveness  is confirmed by numerical simulations.
After revision:  The results are applied to the Repressilator in synthetic biology, where hyperbolic instability of a unique equilibrium guarantees the persistence of oscillation phenomena in the global sense, and the effectiveness of our linear robust instability analysis is confirmed by numerical simulations.