1 citations · 1 across the 6 of their papers we have counts for
6 papers
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…
Optimal periodic structures with general space group symmetries in the Ohta-Kawasaki problem
Jan Bouwe van den Berg, JF Williams
We consider the problem of rigorously computing periodic minimizers to the Ohta-Kawasaki energy. We develop a method to prove existence of solutions and determine rigorous bounds o…
Spontaneous periodic orbits in the Navier-Stokes flow
Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard +1
In this paper, a general method to obtain constructive proofs of existence of periodic orbits in the forced autonomous Navier-Stokes equations on the three-torus is proposed. After…
Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof
Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard +1
In this paper, we prove existence of symmetric homoclinic orbits for the suspension bridge equation for all parameter values . For each , a p…