Mechanism of Appearing Complex Relaxation Oscillations in a System of Two Synaptically Coupled Neurons

We consider a system of two specially coupled differential-difference equations with delay in the coupling link. We establish that the system has a set of coexisting orbitally asymptotically stable solutions with the total number 2n, n ∈ ℕ, of bursts in the period; moreover, one of the oscillators has m bursts and the other has 2n − m bursts, m = 1,.. , 2n−1. From the results obtained it follows that an additional delay leads to the appearance of coexisting attractors in the system with a given number of bursts in the period. Bibliography: 20 titles. Illustrations: 2 figures. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.