SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 573-607, January 2021.
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we follow solution curves of cycles through folds, checking along the way that a single nondegenerate saddle-node bifurcation occurs. Similarly, we rigorously continue solution curves of cycles starting from their onset at a Hopf bifurcation. We use a blowup analysis to regularize the continuation problem near the Hopf bifurcation point. This extends the applicability of validated continuation methods to the mathematically rigorous computational study of bifurcation problems.

中文翻译：

---

通过去奇化和连续性对Hopf分叉进行严格验证

SIAM应用动力系统杂志，第20卷，第2期，第573-607页，2021
年1月。在本文中，我们提出了一种通用方法，用于严格验证ODE系统中周期轨道的Hopf分叉和鞍节点分叉。通过分析估计和计算机辅助计算的组合，我们遵循了通过折线的循环的求解曲线，并检查了是否发生单个未退化的鞍形节点分叉。同样，我们严格地从霍普夫分叉处开始的周期继续求解周期的解曲线。我们使用爆炸分析来规范Hopf分叉点附近的连续性问题。这将经过验证的连续方法的适用性扩展到分叉问题的数学严格的计算研究中。