Properties of variations in the periods of ring neural oscillators with noise

Effects of additive noise on a series of the periods of oscillations in unidirectionally coupled ring neural networks of ring oscillator type are studied. Kinematical models of the traveling waves of an inconsistency, i.e. the successive same signs in the states of adjacent neurons in the network, are derived. A series of the half periods in the network of N neuron is then expressed by the sum of N sequences of the N-1st-order autoregressive process, the process with the spectrum of exponential type and the first-order autoregressive process. Noise and the interaction of the inconsistency cause characteristic positive correlations in a series of the half periods of the oscillations. Further, an experiment on an analog circuit of the ring neural oscillator was done and it is shown that correlations in the obtained periods of the oscillations agree with the derived three expressions.