3 papers
math.DS2022
Computer-assisted proofs of Hopf bubbles and degenerate Hopf bifurcations
Kevin Church, Elena Queirolo
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…
math.NA2020
Rigorous validation of a Hopf bifurcation in the Kuramoto-Sivashinsky PDE
Jan Bouwe van den Berg, Elena Queirolo
We use computer-assisted proof techniques to prove that a branch of non-trivial equilibrium solutions in the Kuramoto-Sivashinsky partial differential equation undergoes a Hopf bif…
math.DS2020
Rigorous verification of Hopf bifurcations via desingularization and continuation
Jan Bouwe van den Berg, Jean-Philippe Lessard, Elena Queirolo
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…