Harmonic Oscillators with Nonlinear Damping
J. C. Sprott
Department of Physics, University of Wisconsin-Madison,
Madison, Wisconsin 53706, USA
sprott@physics.wisc.edu
W. G. Hoover
Ruby Valley Research Institute, Highway Contract 60,
Box 601, Ruby Valley, Nevada 89833, USA
hooverwilliam@yahoo.com
Received September 10, 2017
ABSTRACT
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.