1. Nonlinear oscillators and chaos

2. Chaotic dynamics

3. β

4. Amplitude of a damped oscillator
Angle
Time

5. Trajectory in phase space
d/dt angle
Angle

6. Forced oscillations

7. Chaotic trajectories in phase space

8. Linear oscillator, no damping, not forced
different I.C.s

9. Nonlinear oscillator, forced, but no damping

10. Snapshots of trajectories in phase space

11. Damped oscillator

12. Deeper analysis of the chaotic pendulum

15. Chaos in real life: two examples

16. Cardiac disorder: chaotic heart beating
heart as a nonlinear oscillator
periodic current pulses produce chaotic motion
(periodic doubling… etc)
helps designing an effective pace maker

17. Chaotic
dripping
faucet

18. Higher dimensional system
Poincare section