Notes to Supplement the Lectures: (.pdf files)

First-Order ODE's: Existence, Stability, and Bifurcations Click here

Second-Order Systems: Phase-Plane Click here

Second-Order Conservative Systems: Bifurcation Click here

Periodic Solutions to Nonlinear Problems: Lyapunov Functions, Poincare-Pendixson, Index Theory Click here

Notes on Reversible Systems (by Simon Tse) Click here

Bifurcations of Perodic Solutions: Hopf Bifurcations Click here

Relaxation Oscillations Click here

Forced Duffing Equation Click here

A Few Notes on Lorenz System Click here

Discrete Maps Click here

Howeworks: (.pdf files)

Homework 1 (Due Jan. 20th): Assignment Click here: Solutions Click here

Homework 2 (Due Jan. 31st) Assignment Click here: Solutions Click here:

Homework 3 (Due Feb. 14th): Assignment Click here: Solutions Click here:

Homework 4: (Due March 7th): Assignment Click here: Solutions Click here:

Midterm: Questions and Solutions Click here:

Homework 5: (Due March 14th): Assignment Click here: Solutions Click here:

Homework 6: (Due March 28th): Assignment Click here: Solutions Click here:

Homework 7: (Due April 7th): Assignment Click here: Solutions Click here:

Lab Information

LSK 121 is for Math 345. You can use the lab at other times when there is an available seat (typically late afternoon is best).

Lab Login, Passwords, and Policy Instructions

Lab1 (Due Jan. 27th): A Fisheries Harvesting Model (The Phase Line:) For the Lab Click Here and for the solutions Click Here The harvest.ode file: Click here The harvestper.ode file: Click here

Lab2 (Due Feb. 7th): Insect Infestation in the Budworm Model (An example of saddle node bifurcations:) For the Lab Click Here and for the solutions Click Here The insect.ode file: Click here

Lab3 (Due Feb. 26th): The Simple Pendulum and a Glider Problem: For the Lab Click Here and for the solutions Click Here The pend.ode file: Click here The glider.ode file: Click here

Lab4 (Due March 26th) The Hopf Bifurcation Theorem and Limit Cycles: For the Lab Click Here and for the solutions Click Here The hopf.ode file: Click here The lotreal.ode file: Click here

Lab5 (Due April 7th) Chaotic Dynamics For the Lab Cick Here The doubwell.ode file: Click here The lorenz.ode file: Click here