Mutual synchronization in 4 coupled oscillators with different natural frequencies

In this paper, we investigate the synchronization phenomena in 4 oscillators with different natural frequencies full-coupled by capacitors. When there is no natural frequency difference among the oscillators, 4-phase oscillation is not stable. In this system, however, because the frequencies of the oscillators have a slight difference, nearly sinusoidal 4-phase oscillations are stably excited. Moreover we have proved the stability of 4-phase solutions by calculating the stability of the fixed points and considered why frequency locking occurs. From the results we can confirm that 4-phase oscillations can be excited when the symmetry of the system collapses