Recently, there has been a great effort to extract the phase of chaotic attractors and complex
oscillators. As a consequence many phases have been introduced, as example the standard
phase θ based on the rotation of the vector position, and the phase ϕ based on the rotation
of the tangent vector. Despite of the large interest in the phase dynamics of coupled
oscillators there is still a lack of approaches that analyze whether these phase are
equivalent and on what conditions these phases work. In this work, we show that the phase …