The generation of double dark resonance and double electromagnatically induced transparency in this energy level system is obtained, its physical mechanism is discussed.

In this thesis, we mainly discuss multiple electromagnetically induced one-photon transparency and double electromagnetically induced two-photon transparency in a five-level inverted-tripod scheme atomic system, and the multi-dark resonances induced by the coherent perturbations as well as the effects of the linewidth of the coupling field on the multi-dark resonances.

By using averaging method for nonlinear oscillation, internal resonance, primary resonance,and double resonances of the first order approximation solutions and their corresponding steady state solutions of the system are obtained.

According to the method of multiple scales for nonlinear oscillations, the double resonances of magnetism and solid coupling of hydroelectric_generator stator system were investigated.