Duffing Oscillator

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The Duffing oscillator moves in a double well potential, sometimes characterized as nonlinear elasticity, with sinusoidal external forcing. It is described by the equation . We consider the parameters , , , , , and . Solutions to the oscillator equation can exhibit extreme nonlinear dynamics, including limit cycles, strange attractors, and chaotic behavior. The system is, as expected, highly sensitive to the initial conditions.

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When the periodic force () that drives the system is large, the motion can become chaotic and the phase space diagram can develop a strange attractor. A Poincaré section can be plotted by taking one phase space point in each period of the driving force. In the simplest cases, when the system enters a limit cycle, the Poincaré section reduces to a single point. A strange attractor is usually associated with a complicated fractal curve.

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Contributed by: Housam Binous and Nasri Zakia (March 2011)
Open content licensed under CC BY-NC-SA


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