Duffing Oscillator Circuit
This is an electronic circuit that simulates a particle in a Duffing potential. You can "drive" the particle with an external voltage, changing frequency and amplitude, and you can measure the resulting position and velocity of the particle. At some drive parameters, the motion of the particle becomes chaotic. Interesting investigations could include creation of Poincare plots of the strange attractor, mapping bifurcations, and determination of Lyapunov exponent at different drive parameters.
This circuit was first tested by Carleene Busse in the fall of 2012, the current apparatus was built by Eric Ayars. It works acceptably, but there is currently an unexplained asymmetry in the circuit that makes one lobe preferential to the other. This asymmetry does not break the experiment, but finding a fix for the problem would be nice.
Reading
- Analogue Electrical Circuit for Simulation of the Duffing-Holmes Equation (Original paper from which the circuit was constructed)
- Dynamical symmetry breaking and chaos in Duffing's equation
- A unit on oscillations, determinism and choas for introductory physics students
- Read enough of one of the books on chaos in 108 that you know what all the terms in the above description mean.
Questions
- What is phase space, and what should a phase space plot look like for a Duffing oscillator in a stable repeating 'orbit'?
- What is a Poincare plot?
- What are bifurcations, and why are they interesting in the context of chaos?
Hazards
None.
Location
Room 108, Cabinet 108.12