Constructing Chaotic Systems with Total Amplitude Control
Chunbiao Li
School of Electronic & Information Engineering,
Nanjing University of Information Science & Technology,
Nanjing 210044, P. R. China
Engineering Technology Research and Development
Center of Jiangsu, Circulation Modernization Sensor Network,
Jiangsu Institute of Commerce, Nanjing 211168, P. R. China
Julien Clinton Sprott
Department of Physics, University of Wisconsin -- Madison,
Madison, WI 53706, USA
Zeshi Yuan and Hongtao Li
School of Electronic and Optical Engineering
Nanjing University of Science and Technology
Nanjing 210094, P. R. China
Received: February 27, 2015
ABSTRACT
A general method is introduced for
controlling the amplitude of the variables in chaotic systems by
modifying the degree of one or more of the terms in the
governing equations. The method is applied to the Sprott B
system as an example to show its flexibility and generality. The
method may introduce infinite lines of equilibrium points, which
influence the dynamics in the neighborhood of the equilibria and
reorganize the basins of attraction, altering the
multistability. However, the isolated equilibrium points of the
original system and their stability are retained with their
basic properties. Electrical circuit implementation shows the
convenience of amplitude control, and the resulting oscillations
agree well with results from simulation.