Affiliation:
1. Regional Scientific and Educational Mathematical Center «Centre of Integrable Systems», P. G. Demidov Yaroslavl State University, 150003 Yaroslavl, Russia
Abstract
We studied travelling waves in N nonlinear differential equations with a delay and large parameter. This system is important because it can be regarded as a phenomenological model of N-coupled neuron-like oscillators with delay. The problem of the existence of travelling-wave-type solutions was reduced to the study of the dynamics of an auxiliary equation with two delays. Using a special asymptotic method for the large parameter we proved that this equation has a relaxation cycle, studied its properties (amplitude, period and asymptotics) and found the sufficient stability conditions. Based on this periodic solution the travelling waves of the initial model were constructed.
Funder
Russian Science Foundation
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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