Week

Date

Topics covered

1

Jan 12-16

Introduction: nonlinear dynamics, complex systems; 1-dimensional flows and stability

2

Jan 19-23

elementary bifurcations: saddle-node, pitchfork; 2-dimensional flows: linear systems 

HW#1 due wednesday

3

Jan 26-30

2-dimensional flows: phase space analysis, limit cycle; synchronization

HW#2 due wednesday

4

Feb 2-6

maps: stability, periodic orbits, logistic map: bifurcation diagram, periodic windows, crisis; Lyaunov exponent 

HW#3 due wednesday

5

Feb 9-13

Fractals and their quantification, dimension algorithms; Lorenz system, strange attractor 

HW#4 due friday

Final Exam:  TBD in class