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 |
Jan 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 Monday, Feb 19 |
| 7 |
Feb 26-1 |
Lorenz system, strange attractor, Lyapunov exponent Project outline due on Monday, Feb 26 EXAM: Friday, March 1 |
| 8 |
Mar 4-8 |
maps: stability, periodic orbits, logistic map:
bifurcation diagram, periodic window, crisis HW#6 due friday |
| 9 |
Mar 11-15 |
FINALLY!!!!! SPRING BREAK |
| 10 |
Mar 18-22 |
renormalization; Fractals and
their quantification, dimension algorithms Project simulation due monday, march 18 |
| 11 |
Mar 25-29 |
multi-fractal, Baker's map, Henon map HW#7 due friday Last day to withdraw - on friday |
| 12 |
Apr 1-5 |
unstable periodic orbit, stable and unstable manifold,
bistable system |
| 13 |
Apr 8-12 |
embedding theorem, applications to time series analysis,
symbolic dynamics Paper due on Monday, April 8 |
| 14 |
Apr 15-19 |
control of chaos, shadowing
lemma HW#8 due friday |
| 15 |
Apr 22-26 |
spatiotemporal
systems Student project presentations |
| 16 |
Apr 29-3 |
April 29: Last day of instruction |