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Applied and Computational Math Seminar

Hopf bifurcation in PDE 

Elena Queirolo, Vrije University 

Location:  Hill 425
Date & time: Friday, 04 October 2019 at 12:00PM - 1:00PM

Abstract: In this talk we will use validated numerics to prove the existence of a Hopf bifurcation in the Kuramoto-Sivashinky PDE.

Validated numerics, in particular the radii polynomial approach, allows to prove the existence of a solution to a given problem in the neighborhood of a numerical approximation. A known use of this technique is for branch following in parameter dependent ODEs. In this talk, we will consider periodic solutions of polynomial ODEs.

With a blow up approach, we can rewrite the original ODE into a new system that undergoes a saddle node bifurcation instead of a Hopf bifurcation, thus avoiding the singularity of the periodic solution. We can then prove the existence of a Hopf bifurcation in the original system with a combination of analytical and validated numeric results.

To conclude, we will apply the same techniques in the Kuramoto-Sivashinky case, thus demostrating the flexibility of this approach.

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