Stability of coupled Huygens oscillators

The orbits resulting from perturbations of a limit cycle of an Andronov clock remain close to the original unperturbed limit cycle. In particular, when we have a number N > 2 of isolated Andronov clocks put in interaction at instant t = 0, exchanging small perturbations between them, the resulting perturbed orbits in the product phase space remain close to the original torus of the set of isolated Andronov clocks. We obtain the Arnold tongues for the Huygens coupling of two clocks one with frequency omega and the other with frequency $ N \omega +\varepsilon $ N omega+epsilon, where N is a positive integer and $ \varepsilon \gt 0 $ epsilon > 0 is a small real number.

Automated summary

This paper investigates the effects of perturbations and interactions of Andronov clocks on the orbits, and finds that the resulting perturbed orbits are very close to the unperturbed orbits. The Arnold tongues for Huygens coupling are obtained through experiments.