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 1822 
1dimensional flows, stability analysis, steady state
classification, elementary bifurcations: saddlenode, transcritical No HW due this week ! 
3 
Jan 2529 
elementary bifurcations: pitchfork 2dimensional flows: linear systems, classification, phase space analysis HW#1 due friday Last day to drop  on friday 
4 
Feb 15 
limit cycles, PoincareBendixson theorem, excitable systems HW#2 due friday 
5 
Feb 812 
Bifurcations: elementary bifurcations, sub (super) critical
Hopf bifurcations, global bifurcations HW#3 due friday 
6 
Feb 1519 
Lorenz system, strange attractor, Lyapunov exponent HW#4 due friday 
7 
Feb 2226 
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 711 
Fractals and their quantification, dimension algorithms,
multifractal HW#6 due friday Project outline due on Wednesday, March 9 Last day to withdraw  on friday 

9 
Mar 1418 
FINALLY!!!!! SPRING BREAK 
10 
Mar 2125 
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 48 
composite fractals, embedding theorem, applications to timeseries analysis 
13 
April 1115 
symbolic dynamics and timeseries analysis 
14 
Apr 1822 
control of chaos, synchronization Paper due on Monday, April 18 
15 
Apr 25  29 
shadowing lemma, spatiotemporal systems 
16 
May 26 
May 2: Last day of instruction 