Slow-Fast Systems with an Equilibrium Near the Folded Slow Manifold

被引：0

作者：

Gelfreikh, Natalia G. ^{[1
]}

Ivanov, Alexey V. ^{[1
]}

机构：

[1] St Petersburg State Univ, 7-9 Universitetskaya Nab, St Petersburg 199034, Russia

来源：

REGULAR & CHAOTIC DYNAMICS | 2024年 / 29卷 / 02期

关键词：

slow-fast systems; period-doubling bifurcation; SINGULAR PERTURBATION-THEORY; STABILITY LOSS; OSCILLATIONS; PERSISTENCE;

D O I：

10.1134/S156035472354002X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a slow-fast system with two slow and one fast variables.We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighborhood of the fold. We derive a normal form for the systemin a neighborhood of the pair "equilibrium-fold"and study the dynamics of the normal form. In particular, as the ratio of two time scales tends to zero we obtain an asymptotic formula for the Poincare mapand calculate the parameter values for the first period-doubling bifurcation. The theory is applied to a generalization of the FitzHugh - Nagumo system.

引用

页码：376 / 403

页数：28

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