Tiago Pereira
Dynamics on Complex Networks
Bifurcation Theory
Tuesday & Friday : 2pm - 4pm ICMC 5-004
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
Departamento de Matematica Aplicada e Estatistica
Office 3-242
Phone: +55 16 33736711
Email: tiago at icmc.usp.br
UNIVERSIDADE DE SÃO PAULO
INSTITUTO DE CIÊNCIAS MATEMÁTICAS E DE COMPUTAÇÃO
Avenida Trabalhador São-carlense, 400 - Centro
CEP: 13566-590 - São Carlos - SP