  Strong coupling regime takes place in open hybrid systems consisting of two
or more physical subsystems when the coupling strength between subsystems
exceeds the relaxation rate. The relaxation arises due to the interaction of
the system with environment. For this reason, it is usually believed that the
enhancement of the interaction with environment inevitably leads to a
transition of the system from the strong to weak coupling regime. In this
paper, we refute this common opinion. We demonstrate the interaction of the
coupled system with environment induces an additional coupling between the
subsystems that contribute to retention the system in the strong coupling
regime. We show that the environmental-induced coupling strength is
proportional to the product of the Rabi coupling strength by the gradient of
the density of states of the reservoir. There is a critical Rabi coupling
strength above which the environmental-induced coupling ensures that the system
remains in the strong coupling regime at any relaxation rate. In this case, the
strong coupling regime takes place even when the relaxation rate is
significantly above the Rabi coupling strength between the subsystems. The
critical coupling depends on the gradient of the reservoir density of states.
We demonstrate that managing this gradient can serve as an additional tool to
control the properties of the coupled systems.
