Tentative weekly course calendar for Phys648 (3 lectures per week)

Week Date Topics covered
1
Jan 15
Introduction: nonlinear dynamics, complex systems, interdisciplinary science
2
Jan 18-22
1-dimensional flows, stability analysis, steady state classification, elementary bifurcations: saddle-node, transcritical
No HW due this week !
3
Jan 25-29
elementary bifurcations: pitchfork
2-dimensional flows: linear systems, classification, phase space analysis
HW#1 due friday
Last day to drop - on friday
4
Feb 1-5
limit cycles, Poincare-Bendixson theorem, excitable systems
HW#2 due friday
5
Feb 8-12
Bifurcations: elementary bifurcations, sub- (super-) critical Hopf bifurcations, global bifurcations
HW#3 due friday
6
Feb 15-19
Lorenz system, strange attractor, Lyapunov exponent
HW#4 due friday
7
Feb 22-26
maps: stability, periodic orbits, logistic map
HW#5 due friday
Project topic due on wednesday, Feb 24
8
Feb 29- 4
logistic map: bifurcation diagram, periodic window, crisis, renormalization
No HW due this week
EXAM: Friday, March 4

Mar 7-11
Fractals and their quantification, dimension algorithms, multi-fractal
HW#6 due friday
Project outline due on Wednesday, March 9
Last day to withdraw - on friday
9
Mar 14-18
FINALLY!!!!! SPRING BREAK
10
Mar 21-25
Baker's map, Henon map
HW#7 due friday
11
Mar 28 - Apr 1
unstable periodic orbit, stable and unstable manifold, bistable system
HW#8 due friday
Project simulation due on Wednesday, March 30
12
Apr 4-8
composite fractals, embedding theorem, applications to timeseries analysis
13
April 11-15
symbolic dynamics and timeseries analysis
14
Apr 18-22
control of chaos, synchronization
Paper due on Monday, April 18
15
Apr 25 - 29

shadowing lemma, spatiotemporal systems
Students' project presentations
 

16

May 2-6

May 2: Last day of instruction
FINAL: Tuesday, May 3, 1-3pm ....... Good success !!