Multistability and Bursting in a Pair of Delay Coupled Oscillators with a Relay Nonlinearity

We consider a system of two relay type differential-difference equations, with delay in the coupling between oscillators. The equations are coupled in a special way. The system models an association of coupled neural oscillators. An important feature of the system is an additional delay in the connection chain. The delay allows obtaining new effects which is an essential complication of the system dynamics, and an appearance of coexisting special form attractors. We show that there coexist asymptotically orbitally stable solutions with summary 2n (n is an element of N) spikes on a period. Moreover, the first oscillator has m spikes, and the second one has 2n - m (m = 1, 2, ..., 2n - 1) spikes on a period. We conclude that the additional delay leads to an accumulation of coexisting attractors with a given number of spikes on a period. Copyright (C) 2019. The Authors. Published by Elsevier Ltd. All rights reserved.