| Abstract: |
| In this talk, we want to present methodologies for a validated numerics approach to studying bifurcations in ODEs and PDEs. We are interested both in proving the existence of a bifurcation and in having a grasp of dynamics near it. We will present a generalised approach to validate saddle node bifurcations that we will apply both to ODEs and PDEs. With this framework in mind, we can then reformulate Hopf bifurcations as bifurcations where the perturbation of the solution undergoes a saddle node bifurcation. After presenting some applications of this rewriting, we will present recent advances on how pitchfork bifurcations can also fit into a similar framework. |
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