In this work we study the dynamics of a nonlinear system, consisting of coupled resonators, and provide stability analysis of possible states. Such kind of an open system can be described in terms of the normal modes, namely, the bright and the dark ones. The dark mode has zero radiative losses and it is not coupled to the far field, so it can not be directly excited by the pump, however it be formed due to a symmetry break and nonlinear interaction with the bright mode. We demonstrate the existence of the stable hybrid state, as well as the self-oscillatory regime. We also show the possibility of the energy locking, when the pump is switched off, but the dark mode still has a non-zero amplitude for some period of time, defined by non-radiative losses. These results may be used for the realization of optical devices based on the dark modes, such as memory elements or frequency combs.

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