Recommended Textbook: Invitation to Dynamical Systems
Author: Edward R. Scheinerman
Online pdf version: m4067-book.pdf
Course Notes: Notes will also be provided for parts of course
Prerequisite: Math 2066 (Differential Equations) and first two years of the Math program
Instructor: Dr. B.G. Adams Office: FA-378 Phone: 675-1151 x 2323 Email: badams at cs dot laurentian dot ca
Lecture Times: Tues-Thurs: 1:00-2:30, Room: C-306
The final grade will be determined on the basis of
Assignments 25% 2 Class Tests (Feb 10, Mar 24) 25% Final exam (3 hours) 50%
Note: To download the maple worksheets (mw extension) right click on the link and choose "Save Target As".
Review of first order DE's:
Notes first-order.pdf Maple worksheet (exact solutions) diffeq1-exact.mw diffeq1-exact.html Maple worksheet (numerical solutions) diffeq1-numeric.mw diffeq1-numeric.html Logistic equation diffeq1-logistic.mw diffeq1-logistic.html Logistic equation with threshold diffeq1-logistic2.mw diffeq1-logistic2.html Direction fields and solutions using DEplot directionfield.mw directionfield.html
Review of Linear Systems of DE's:
Some Maple Recipes for Linear Systems of DE's maplede.pdf Linear mass/spring and pendulum problems spring.pdf Notes on Linear Systems of Differential Equations linsys.pdf Exact solution of system of 2 first order DE's diffeq2e.mw diffeq2e.html Numerical solution of system if 2 first order DE's diffeq2n.mw diffeq2n.html Phase portrait for a saddle point phase1.mw phase1.html Phase portrait for a saddle point phase1b.mw phase1b.html Phase portrait for a center phase2.mw phase2.html Phase portrait for an unstable node phase3.mw phase3.html
Nonlinear systems and pendulum using Maple
Nonlinear phase plane example section3-2-2a.mw section3-2-2a.html Time dependence for small and large angles pendulum1.mw pendulum1.html Phase plane analysis pendulum2.mw pendulum2.html Phase plane analysis, damped pendulum pendulum3.mw pendulum3.html Phase plane analysis, damped pendulum dampedpendulum.mw dampedpendulum.html Phase plane analysis, damped pendulum, strong and weak damping damped.mw damped.html
Contour plots using Maple
Contour plots for a non-linear system contour1.mw contour1.html Contour plots for undamped pendulum undampedpendulum.mw undampedpendulum.html
Competing Species Model
Peaceful Coexistence competition1.mw competition1.html Extinction of one species competition2.mw competition2.html
Predator Prey Model
Phase Plane Analysis predator-prey.mw predator-prey.html Phase Plane and Time Series (Rabbits and Foxes) rabfox.mw rabfox.html
Lyapunov functions
Inconclusive example (numerical) spiral.mw spiral.html Unstable limit cycle limitcycle.mw limitcycle.html
Gradient systems
3-D plot example gradient-1.mw gradient-1.html gradient plot (vector field) gradient-2.mw gradient-2.html
Limit Cycles
Unit circle as limit cycle limitcycle.mw limitcycle.html Van der Pol equations (1) vanderpol.mw vanderpol.html Van der Pol equations (2) vanderpol-2.mw vanderpol-2.html
Bifurcations
Hopf bifurcation (1) bifurcation.mw bifurcation.html Hopf bifurcation (2) bifurcation-2.mw bifurcation-2.html
Chaos in the Lorenz System
Period doubling and chaos lorenz.mw lorenz.html
1D Discrete Maps
Attractive 2cycle for the map 1 - x2 example1a.mw example1a.html Numerical iteration of the map 1 - x2 example1b.mw example1b.html Analysis of the map 1 - x2 example.mw example.html Iterating the tent map tentorbit.mw tentorbit.html Graphical analysis of the tent map tentgraph.mw tentgraph.html Logistic map bifurcation diagram logistic.pdf Period 4 for map x2 + a period4.mw period4.html Period 3 for map x2 + a period3.mw period3.html Graphical iteration for map x2 + a squaremapiter.mw squaremapiter.html Bifurcation diagram for map x2 + a square.pdf Time series for map x2 + a squaring-time-series.pdf Time series differences for map x2 + a squaring-time-series-diff.pdf Numerical iteration of map x2 + a squaremaporbit.mw squaremaporbit.html Time series map x2 + a squaremaptime.mw squaremaptime.html Sensitvity for map x2 + a squaremaptime-diff.mw squaremaptime-diff.html Symbolic dynamics for map x2 + a symbolics.mw symbolics.html
2D Discrete Maps
Computing matrix powers matrix-powers.mw matrix-powers.html Fixed points if 2-D maps fixedpoints.mw fixedpoints.html Orbits of 2-D maps maporbit2d.mw maporbit2d.html mapphase2d.mw mapphase2d.html Henon map composition henon-map.mw henon-map.html Iterating the enon map trapping quadrilateral henon-quadrilateral.mw henon-quadrilateral.html Henon map attractor henon1.pdf henon2.pdf henon3.pdf
Affine systems
Notes on symbolic dynamics symbolic.pdf Evolution of Sirepinski triangle sierpinski.pdf Evolution of Koch snowflake koch1.pdf Contraaction maps specnorm.mw specnorm.html specnorm2.mw specnorm2.html specnorm3.mw specnorm3.html specnorm4.mw specnorm4.html specnorm5.mw specnorm5.html IFS for fractal fern fernifs0.pdf fernifs1.pdf fernifs2.pdf fernifs3.pdf fernifs4.pdf fernifs5.pdf fernifs.pdf
Deterministic IFS algorithm
Single point images sierpinski-1.mw sierpinski-1.html Full square images sierpinski-2.mw sierpinski-2.html X fractal x.mw x.html deterministic-ifs.mw deterministic-ifs.html
Random iteration algorithm
Notes on chaos game sierp.pdf crules.pdf calg.pdf Results for sierpinski triangle sierpinski-chaos.pdf Maple results chaos.mw chaos.html X fractal random-iteration.mw random-iteration.html W fractal random-wfractal.mw random-wfractal.html
Area probability random iteration algorithm
W fractal proportional-wfractal.mw proportional-wfractal.html Properties of affine maps affine.pdf Area probability calculations probability-1.pdf probability-2.pdf Fern algorithm fern.pdf Fern fractal proportional-fern.mw proportional-fern.html