Harmonic Oscillators with Nonlinear Damping

J. C. Sprott
Department of Physics, University of Wisconsin-Madison,
Madison, Wisconsin 53706, USA

W. G. Hoover
Ruby Valley Research Institute, Highway Contract 60,
Box 601, Ruby Valley, Nevada 89833, USA

Received September 10, 2017


Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

Ref: J. C. Sprott and W. G. Hoover, International Journal of Bifurcation and Chaos 27, 1730037 (2017)

The complete paper is available in PDF format.

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