霍普夫气泡与退化霍普夫分岔的计算机辅助证明

Church Kevin, Queirolo Elena

Université de Montréal, Montreal, Canada.

Technische Universität München, Munich, Germany.

J Dyn Differ Equ. 2024;36(4):3385-3439. doi: 10.1007/s10884-023-10279-x. Epub 2023 Jul 4.

We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate Hopf bifurcations in ordinary and delay differential equations. We apply the method to rigorously investigate these nonlocal orbit structures in the FitzHugh-Nagumo equation, the extended Lorenz-84 model and a time-delay SI model.

我们提出了一种计算机辅助方法，以证明常微分方程和时滞微分方程中Hopf气泡和退化Hopf分岔的存在性。我们将该方法应用于严格研究FitzHugh-Nagumo方程、扩展的Lorenz-84模型和一个时滞SI模型中的这些非局部轨道结构。