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

Week Date Topics covered
1
Jan 16-19
Introduction: nonlinear dynamics, complex systems, interdisciplinary science; 1-dimensional flows, stability analysis
2
Jan 22-26
steady state classification, elementary bifurcations: saddle-node, transcritical, pitchfork
HW#1 due friday
Last day to drop - on friday
3
Feb 29-2
2-dimensional flows: linear systems, classification, nonlinear systems, phase space analysis
HW#2 due friday
4
Feb 5-9
conservative systems, time-reversal symmetry;
HW#3 due friday
5
Feb 12-16
limit cycles, Poincare-Bendixson theorem, excitable systems, synchronization
HW#4 due friday
6
Feb 19-23
Bifurcations: elementary bifurcations, sub- (super-) critical Hopf bifurcations, global bifurcations
HW#5 due friday
Project topic due on wednesday, Feb 21
7
Mar 26-2
Lorenz system, strange attractor, Lyapunov exponent
EXAM: Friday, March 2
8
Mar 5-9
maps: stability, periodic orbits, logistic map: bifurcation diagram, periodic window, crisis
HW#6 due friday
Project outline due on Wednesday, March 7
9
Mar 12-16
FINALLY!!!!! SPRING BREAK
10
Mar 19-23
renormalization; Fractals and their quantification, dimension algorithms
HW#7 due friday
11
Mar 26-30
multi-fractal, Baker's map, Henon map
HW#8 due friday
Project simulation due on Wednesday, March 28

Last day to withdraw - on friday
12
Apr 2-6
unstable periodic orbit, stable and unstable manifold, bistable system
13
Apr 9-13
embedding theorem, applications to timeseries analysis, symbolic dynamics
Paper due on Wednesday, April 11
14
Apr 16-20
control of chaos, shadowing lemma 
15
Apr 23-27
spatiotemporal systems
Student project presentations
16
May 30-4

April 30: Last day of instruction
FINAL: Thursday, May 3, 1-3pm ....... Good success !!