标题： FitzHugh-Nagumo方程：从全局动力学到慢-快系统 显示英文标题

标题： FitzHugh-Nagumo equation: from global dynamics to slow-fast system

摘要： 我们关注三参数FitzHugh-Nagumo族及其紧化问题的定性研究。 我们根据参数将研究分为三种情形。 其中一种情形的特点是存在具有Z2对称性的双零分岔（余维二的奇点）。 在这种情况下，我们明确地展示出展开余维二奇点的尖点、霍普夫、贝利亚科夫和双同宿分岔/转变曲线，并绘制出分岔图。 我们将此分析与相关的慢-快族理论以及canards的存在性联系起来。 我们通过考虑该族相图的全局紧化来完成本研究。 本研究补充了Georgescu、Rocsoreanu和Giurgic Teanu在"Global Bifurcations in FitzHugh-Nagumo Model"中总结的工作，收录于Trends in Mathematics: Bifurcations, Symmetry and Patterns (2003)。 显示英文摘要

摘要： We concentrate our attention on the qualitative study of the phase portraits of the three-parameter FitzHugh-Nagumo family and its compactification. We divide the study into three scenarios based on the parameters. One of the scenarios is characterised by the existence of a double-zero bifurcation with Z2 symmetry (a singularity of codimension two). In this case, we explicitly exhibit the pitchfork, Hopf, Belyakov, and double homoclinic bifurcation/transition curves unfolding the singularity of codimension two and plot the bifurcation diagrams. We bridge this analysis with the theory on the associated slow-fast family and the existence of canards. We complete our study with the global compactification of the phase portraits for the family under consideration. This study complements the work summarised in Georgescu, Rocsoreanu and Giurgic Teanu, "Global Bifurcations in FitzHugh-Nagumo Model", Trends in Mathematics: Bifurcations, Symmetry and Patterns (2003).