Nonisochronism of one oscillator in a system of two coupled nonlinear oscillators leads to an overlap of synchronous and asynchronous regimes. In some cases, two-frequency oscillations may completely destroy synchronization. We derive conditions for the emergence of these competitive two-frequency oscillations and for the destruction of the synchronous regime, which occurs due to the merging of stable and unstable fixed points in phase space. Analysis is done by reducing the averaged coupled oscillator equations to the general nonlinear pendulum equation. Boundaries of each regime derived in this way are in good agreement with those obtained numerically.

• Received 9 November 1990

DOI:https://doi.org/10.1103/PhysRevA.43.5638