Linearization of the Lorenz System

Chunbiao Li
School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China
Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Commerce, Nanjing 211168, China

Julien Clinton Sprott
Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA

Wesley Thio
Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA

Received 24 November 2014
Received in revised form 6 January 2015
Accepted 7 January 2015
Available online 13 January 2015
Communicated by C.R. Doering

A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system.

Ref: C. Li, J. C. Sprott, and W. Thio, Phys. Lett. A 379, 888-893 (2015)

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