Computer-assisted proofs of Hopf bubbles and degenerate Hopf bifurcations

2022/02/27 by Kevin E. M. Church, Church, Kevin, Elena I. Queirolo +1
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2202.13326

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.

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