Computer-assisted proofs of Hopf bubbles and degenerate Hopf bifurcations

Abstract

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 bifurcation structures in the FitzHugh-Nagumo equation, the extended Lorenz-84 model and a time-delay SI model.