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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…
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…