Offset Boosting for Breeding Conditional Symmetry

Chunbiao Li∗
Jiangsu Collaborative Innovation Center of Atmospheric Environment and
Equipment Technology (CICAEET), Nanjing University of Information
Science and Technology, Nanjing 210044, P. R. China
Jiangsu Key Laboratory of Meteorological Observation
and Information Processing, Nanjing University
of Information Science and Technology,
Nanjing 210044, P. R. China
[email protected]
[email protected]

Julien Clinton Sprott
Department of Physics, University of Wisconsin�Madison,
Madison, WI 53706, USA
[email protected]

Yongjian Liu
Guangxi Colleges and Universities Key Laboratory
of Complex System Optimization and Big Data Processing,
Yulin Normal University, Yulin, Guangxi 537000, P. R. China
[email protected]

Zhenyu Gu� and Jingwei Zhang�
Jiangsu Key Laboratory of Meteorological Observation
and Information Processing, Nanjing University
of Information Science and Technology,
Nanjing 210044, P. R. China
School of Electronic and Information Engineering,
Nanjing University of Information Science and Technology,
Nanjing 210044, P. R. China
�[email protected]
�[email protected]

Received April 27, 2018; Revised July 5, 2018

Symmetry is usually prevented by the broken balance in polarity. If the offset boosting returns the balance of polarity when some of the variables have their polarity reversed, the corresponding system becomes conditionally symmetric and in turn produces coexisting attractors with that type of symmetry. In this paper, offset boosting in one dimension or in two dimensions in a
3D system is made for producing conditional symmetry, where the symmetric pair of coexisting attractors exist from one-dimensional or two-dimensional offset boosting, which is identified by the basin of attraction. The polarity revision from offset boosting provides a general method for constructing chaotic systems with conditional symmetry. Circuit implementation based on FPGA verifies the coexisting attractors with conditional symmetry.

Ref: C. Li, J. C. Sprott, Y. Liu, Z. Gu, and J. Zhang, International Journal of Bifurcation and Chaos 28, 185013-1-13 (2018)