Crisis in Amplitude Control Hides in Multistability
Chunbiao Li
Jiangsu Key Laboratory of Meteorological Observation and
Information Processing,
Nanjing University of Information Science & Technology,
Nanjing 210044, P. R. China
School of Electronic and Information Engineering,
Nanjing University of Information Science and Technology,
Nanjing 210044, P. R. China
Julien Clinton Sprott
Department of Physics, University of Wisconsin-Madison,
Madison, WI 53706, USA
Hongyan Xing
Jiangsu Key Laboratory of Meteorological Observation and
Information Processing,
Nanjing University of Information Science & Technology,
Nanjing 210044, P. R. China
School of Electronic and Information Engineering,
Nanjing University of Information Science and Technology,
Nanjing 210044, P. R. China
Received: May 15, 2016; Revised September 10, 2016
ABSTRACT
A crisis of amplitude control can
occur when a system is multistable. This paper proposes a new
chaotic system with a line of equilibria to demonstrate the
threat to amplitude control from multistability. The new
symmetric system has two coefficients for amplitude control, one
of which is a partial amplitude controller, while the other is a
total amplitude controller that simultaneously controls the
frequency. The amplitude parameter rescales the basins of
attraction and triggers a state switch among different states
resulting in a failure of amplitude control to the desired
state.