Measure synchronization transition and its critical behavior in coupled camphor rotors

Building upon prior experimental research on measure synchronization (MS) in two coupled camphor rotors [Jain et al., Phys. Rev. E 108, 024217 (2023)], this paper presents an extensive theoretical study on MS transitions in both two and three coupled camphor rotors. For modelling, each camphor rotor is represented by a point particle that is confined to move along a unit circle around their centers, the camphor rotors are coupled with each other through interaction terms described by the repulsive Yukawa potential in between any two point particles. We find that by increasing the coupling intensity in between the camphor rotors, above certain critical coupling intensities, the camphor rotors achieve MS, including partial MS (PMS) and complete MS (CMS). The energy characteristics of MS in the camphor rotors are discussed. The results show that both phase locking and frequency locking are achieved at MS transitions. In addition, through Poincaré cross section analysis, we reveal the dynamic mechanism of various MS transitions.