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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…
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…
More on the parameterization method for center manifolds
Jan Bouwe van den Berg, Wouter Hetebrij, Bob Rink
In a previous paper we generalized the parameterization method of Cabré, Fontich and De la Llave to center manifolds of discrete dynamical systems. In this paper, we extend this re…