Pattern Recognition in Coupled Oscillators with the Phase Coherency Output

It is clarified that the coupled oscillator system, which has the output of the phase coherency, can learn mapping from specified phase patterns to specified phase coherencies. The system considered here has the output unit which is a group of oscillators coupled both to the other oscillators of the system and also to the mean field generated by the output unit itself. It is analytically and numerically shown that the system can learn the above specified mapping. The effect of the distribution of the natural frequency of oscillators on the dynamics of the system is also investigated. It is shown that the system exhibits oscillatory and complex (chaotic) output when the phase pattern sufficiently different from the learned patterns is input into the system.