Nonlinear oscillators and chaos

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Presentation transcript:

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

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