Travelling Waves in the Ring of Coupled Oscillators with Delayed Feedback

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 phenomenological model of N-coupled neuron-like oscillators delay. The problem the existence travelling-wave-type solutions was reduced to study dynamics an auxiliary equation two delays. Using special asymptotic method for parameter we proved that this has relaxation cycle, its properties (amplitude, period asymptotics) found sufficient stability conditions. Based on periodic solution initial were constructed.