Bifurcation Theory

Tuesday & Friday : 2pm – 4pm ICMC 5-004

Program

August

13 – Discussion and Examples.

16 – Persistence of Fixed Points

20 – Proof of  Center Stable/Unstable Manifolds

23 – Proof of  Center Stable/Unstable Manifolds

27 – Proof of  Center Stable/Unstable Manifolds

30 – No lessons

 

September

Homework Projects

– Invariant Foliations

– Smoothness of centre manifolds

– Normal forms – Auto package

 

October

08 – 1d centre manifolds – baby normal forms

11 –  1d centre manifolds – one parameter family

15 –  2d centre manifolds: Hopf Bifurcation 1

22 –  2d centre manifolds: Hopf Bifurcation 2

25 –  2d centre manifolds: SNIC

29 –  2d centre manifolds: Homoclinic

 

November

05 – Homoclinic bifurcation: Shilnikov

08 – Homoclinic bifurcation: Shilnikov

12 – Homoclinic bifurcation: Shilnikov

15 – Coupled Systems with Periodic Motion: Floquet Theory

19 – Coupled Systems with Periodic Motion: Poincare Map

22 – Coupled Systems with Periodic Motion: Phase response

26 – Coupled Systems with Periodic Motion: Averaging Theory

29 – Kuramoto Model

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