Cycles with the embedded bursting effect in a circle of neural oscillators

We consider a model of a circular network of neurons where the functioning of each neuron is described by an equation with two delays. The model under study is a modification considered in the paper of Glyzin et al., where the model of a solitary neuron is based on of the equation with one delay—the Hutchinson equation. We construct discrete traveling waves, i.e., a periodic solution of the system such that all components coincide with the same function shifted by a quantity that is multiple of a certain parameter. To find this solution, we study an auxiliary differential-difference equation of the Volterra type with three delays. For this equation, for any natural \(m\) and \(n\), we establish the existence of a periodic solution that contains \(m\) packets, each of which contains \(n\) bursts per period.