In an effort to mitigate thermoacoustic oscillations in cryogenic distribution systems, the coupled oscillators are established and a phase-tuned tube has been introduced between the system’s distribution branches. The findings indicate that this phase-tuned tube effectively modulates the pressure oscillation state within the distribution pipe. A detailed examination of the phase-tuned tube’s operational mechanism reveals that almost no phase alteration occurs at symmetrical positions proximate to the midpoint, and pressure oscillations remain in a chaotic state, with trajectories exhibiting near-perfect consistency. However, when deviations from the midpoint position increase, the phase disparity between pressure oscillation sequences at symmetrical positions becomes more pronounced. Consequently, the oscillation state transitions into a multi-periodic pattern, although the trajectory remains inconsistent.