Nonlinear oscillators and chaos
Chaotic dynamics
β
Amplitude of a damped oscillator Angle Time
Trajectory in phase space d/dt angle Angle
Forced oscillations
Chaotic trajectories in phase space
Linear oscillator, no damping, not forced different I.C.s
Nonlinear oscillator, forced, but no damping
Snapshots of trajectories in phase space
Damped oscillator
Deeper analysis of the chaotic pendulum
Chaos in real life: two examples
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
Chaotic dripping faucet
Higher dimensional system Poincare section