We engineer mechanical gain (loss) in system formed by two optomechanical cavities (OMCs), that are mechanically coupled. The gain (loss) is controlled by driving the resonator with laser that is blue (red) detuned. We predict analytically the existence of multiple exceptional points (EPs), a form of degeneracy where the eigenvalues of the system coalesce. At each EP, phase transition occurs, and the system switches from weak to strong coupling regimes and vice versa. In the weak coupling regime, the system locks on an intermediate frequency, resulting from coalescence at the EP. In strong coupling regime, however, two or several mechanical modes are excited depending on system parameters. The mechanical resonators exhibit Rabi-oscillations when two mechanical modes are involved, otherwise the interaction triggers chaos in strong coupling regime. This chaos is bounded by EPs, making it easily controllable by tuning these degeneracies. Moreover, this chaotic attractor shows up for low driving power, compared to what happens when the coupled OMCs are both drived in blue sidebands. This works opens up promising avenues to use EPs as a new tool to study collective phenomena (synchronization, locking effects) in nonlinear systems, and to control chaos.
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