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

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.

Ref: C. Li, J. C. Sprott, Z. Yuan, and H. Li, International Journal of Bifurcation and Chaos 25 1530025 (2015)

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