MATH383: A first course in differential equationsApril 9, 2020

Due date: April 23, 2020, 11:55PM.

Bibliography: Trench, Chap 10, DYN lessons

1. Choose parameters $(\delta ,\alpha ,\beta ,\gamma ,\omega )$ of the forced Duffing equation

   ${\displaystyle \ddot{x}+\delta \dot{x}+\alpha x+\beta x^3=\gamma \cos (\omega t),}$

   such that the shows chaotic, period-1, period-2, period-4 behavior. For each case, display the:

   1. Time trajectory $x\left(t\right)$, and velocity function $\dot{x}\left(t\right)$;

   2. Phase portrait of the system;

   3. Poincaré section.