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Travelling Waves in the Ring of Coupled Oscillators with Delayed Feedback
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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.
Title: Travelling Waves in the Ring of Coupled Oscillators with Delayed Feedback
Description:
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.
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