Stability of a stationary solution of a system of activator–inhibitor-type equations with a double-scale internal transition layer

N. T. Levashova, D. S. Samsonov

Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We study boundary value problems for systems of second-order ordinary differential equations with quasimonotonicity conditions typical of problems of activator–inhibitor type and with solutions containing domains with large gradients. We obtain sufficient conditions for the existence of a stable stationary solution. Using the asymptotic method of differential inequalities, we prove the existence and stability theorems.

Keywords: internal transition layer, method of differential inequalities, upper and lower solutions, asymptotic approximation, quasimonotonicity conditions.

PACS: 02.30.Hq

MSC: 34B16

Received: 20.11.2022
Revised: 09.01.2023

DOI: 10.4213/tmf10409

 English version: Theoretical and Mathematical Physics, 2023, 215:2, 691–708

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