A natural synchronization between locomotor and respiratory systems is known to exist for various species and various forms of locomotion. This Locomotor-Respiratory Coupling (LRC) is fundamental for the energy transfer between the two subsystems during long duration exercise and originates from mechanical and neurological interactions. Different methodologies have been used to compute LRC, giving rise to various and often diverging results in terms of synchronization, (de-)stabilization via information, and associated energy cost. In this article, the theory of nonlinear-coupled oscillators was adopted to characterize LRC, through the model of the sine circle map, and tested it in the context of cycling. Our specific focus was the sound-induced stabilization of LRC and its associated change in energy consumption. In our experimental study, participants were instructed during a cycling exercise to synchronize either their respiration or their pedaling rate with an external auditory stimulus whose rhythm corresponded to their individual preferential breathing or cycling frequencies. Results showed a significant reduction in energy expenditure with auditory stimulation, accompanied by a stabilization of LRC. The sound-induced effect was asymmetrical, with a better stabilizing influence of the metronome on the locomotor system than on the respiratory system. A modification of the respiratory frequency was indeed observed when participants cycled in synchrony with the tone, leading to a transition toward more stable frequency ratios as predicted by the sine circle map. In addition to the classical mechanical and neurological origins of LRC, here we demonstrated using the sine circle map model that information plays an important modulatory role of the synchronization, and has global energetic consequences.