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
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:
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Instructions
Detailed ONLINE User Manual
(by Bard Ermentrout). There is no need to print this large file please.
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