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We study evolution of a hierarchical four-body (2+2) system composed by apair of mass-transferring white dwarf binaries. Applying a simplified modelaround the synchronous state of two inner orbital periods, we newly find thatthe four body system could settle down to a limit cycle with a small periodgap. The period gap generates an amplitude variation of emitted gravitationalwaves, as a beat effect. Depending on model parameters, the beat period couldbe 1-10 yr and a large amplitude variation might be observed by spacegravitational-wave detectors.

Coupling of Dual Mass-Transferring White-Dwarf Binaries as a Variable Gravitational-Wave Emitter