Synchronized oscillations of neuro-oscillator systems with mutually exciting connections

A neuro-oscillator system is modeled as a hybrid system containing binary switches. In case of excitatory connected system, oscillations of neuron models synchronize mutually. We give a theoretical interpretation to these synchronizations by using a transformation into a decoupled system. The amplitude and frequency of the limit cycle oscillation are obtained as approximated functions and it is shown how parameters of system affect the oscillations. In numerical simulations, the number of mutually exciting neurons modulates the strength of attractions of the limit cycle.