Bifurcation Theory

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

Warming-up Exercises

Center Manifolds

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