Exactly solvable chaos in an electromechanical oscillator

A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that contr...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2013-09, Vol.23 (3), p.033109-033109
Main Authors: Owens, Benjamin A. M., Stahl, Mark T., Corron, Ned J., Blakely, Jonathan N., Illing, Lucas
Format: Article
Language:English
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Summary:A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological structure similar to either the Lorenz butterfly or Rössler's folded-band oscillator depending on the configuration. Exact solutions are written as a linear convolution of a fixed basis pulse and a sequence of discrete symbols. We find close agreement between the exact analytical solutions and the physical oscillations. Waveform return maps for both configurations show equivalence to either a shift map or tent map, proving the chaotic nature of the oscillations.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4812723