期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
卷 2, 期 4, 页码 851-872出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdss.2009.2.851
关键词
Homoclinic bifurcation; geometric singular perturbation theory; invariant manifolds
资金
- National Science Foundation
- Department of Energy
- Direct For Computer & Info Scie & Enginr
- Division Of Computer and Network Systems [0832782] Funding Source: National Science Foundation
The FitzHugh-Nagumo equation has been investigated with a wide array of different methods in the last three decades. Recently a version of the equations with an applied current was analyzed by Champneys, Kirk, Knobloch, Oldeman and Sneyd [5] using numerical continuation methods. They obtained a complicated bifurcation diagram in parameter space featuring a C-shaped curve of homoclinic bifurcations and a U-shaped curve of Hopf bifurcations. We use techniques from multiple time-scale dynamics to understand the structures of this bifurcation diagram based on geometric singular perturbation analysis of the FitzHugh-Nagumo equation. Numerical and analytical techniques show that if the ratio of the time-scales in the FitzHugh-Nagumo equation tends to zero, then our singular limit analysis correctly represents the observed CU-structure. Geometric insight from the analysis can even be used to compute bifurcation curves which are inaccessible via continuation methods. The results of our analysis are summarized in a singular bifurcation diagram.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据