PERIODICALLY FORCED CHAOTIC SYSTEM
WITH SIGNUM NONLINEARITY
KEHUI SUN
*,†,‡ and J. C. SPROTT
†,§
*School of Physics Science and
Technology,
Central South University,
Changsha
410083, China
†Department of
Physics,
University of Wisconsin Madison,
WI
53706, USA
‡[email protected]
§[email protected]
Received July 10, 2009; Revised August 3, 2009
ABSTRACT
A sinusoidally-driven system
with a
simple signum nonlinearity term is
investigated through an analytical analysis as well as dynamic
simulation. To obtain the
correct Lyapunov exponents, the signum function is replaced by a
sharply varying continuous
hyperbolic tangent function. By phase portraits, Poincar´e
sections and bifurcation diagrams,
the rich dynamic behaviors of this system are demonstrated, such
as an
onion-like strange attractor,
pitchfork and attractor merging bifurcations, period-doubling
routes to
chaos, and chaotic
transients in the case of small damping. Moreover, the chaos
persists
as the damping is reduced to zero.