We have constructed and analyzed a theoretical model of two coupled neural oscillator networks aimed at understanding the underlying basis of phase transitions in biological coordination of rhythmic activities. Each oscillator unit is composed of an excitatory and an inhibitory neuron. These two neurons are coupled to each other forming a negative feedback loop. The excitatory neuron has a self-excitatory connection forming a positive feedback loop. We assume that the change of the coupling strength of the oscillator units or the neurons in each oscillator effects a change in the frequency of the rhythm. We find two, coexisting stable phase-locked modes (in-phase and anti-phase) over a region of coefficients. However, at a critical coupling value, the anti-phase mode becomes unstable and a transition to the in-phase mode occurs. Poincare's method is employed to elucidate bifurcations of the oscillatory solutions, thus revealing the full phase portrait of the network dynamics. The influence of noise on the stability of mode-locked states is also analyzed and correspondence with experimental results is demonstrated.
J. A. Scott Kelso,
"Phase transitions in oscillatory neural networks", Proc. SPIE 1710, Science of Artificial Neural Networks, (1 July 1992); doi: 10.1117/12.140094; https://doi.org/10.1117/12.140094