асимптотика

The purpose of this study is to construct the asymptotics of the relaxation regimes of a system of differential equations with delay, which simulates three diffusion-coupled oscillators with nonlinear compactly supported delayed feedback under the assumption that the factor in front of the feedback function is large enough. Also, the purpose is to study the influence of the coupling between the oscillators on the nonlocal dynamics of the model. Methods. We construct the asymptotics of solutions of the considered model with initial conditions from a special set.

Nonlinear systems of differential equations with delay, which are mathematical models of fully connected networks of impulse neurons, are considered. Purpose of this work is to study the dynamic properties of one special class of solutions to these systems. Large parameter methods are used to study the existence and stability in сonsidered models of special periodic motions – the so-called group dominance or k-dominance modes, where k ∈ N. Results.