Synchronization properties of globally-coupled oscillators including the polarization degree of freedom

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  • 4 March 2004
Abstract
We analyze a system of globally coupled limit-cycle oscillators, considering the polarization degree of freedom, and including randomly distributed natural frequencies and oscillation angles. Increasing the coupling from zero, no polarization order enhancement is possible until the phases start to synchronize, because the phase disorder destroys the interaction among the polarization variables. A transition to phase synchrony is found when the coupling overcomes a critical value, and this transition allows the polarization varibles to interact and synchronize as well. For a given disorder in the natural frequencies two different transitions to synchronization are found. For strong natural angle disorder, the two transitions to phase and polarization synchronization are well separated, and we developed an approximated theory to estimate the phase and polarization order parameters. For weak natural angle disorder, the two transitions merge in a unique process to full synchrony, and we provided the critical coupling for its onset.

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